Bryan Cranston remembers very clearly the day his father broke a man's nose. He was ten, sitting with his elder brother Kyle in the back seat of his father's new car, a car he would soon be forced to sell when the bills mounted up and the acting jobs thinned out, introducing a second-hand replacement one day as if it were an upgrade - Look, kids, rust as standard!

They were driving back to their San Fernando Valley clapboard house. His father, Joe, had just started to turn left when a car arrowed in front of him. The car sped off, but Cranston Sr made chase, honking all the way. "Hey, jackass!" he shouted, stepping out of the car at a stop light. "You almost ran into us!"

The other man got out. "Yeah, and what are you going to do about it, old man?" "Now, my dad," says Cranston to me now. "He was one of those guys with grey hair since he was 30. And he was in his forties at this stage." "Turn the corner," came the reply, "and I'll show you what I'm going to do about it."

They turned the corner, parked up, got out, Cranston's sons still in the backseat watching on. The other guy was tall, in his early twenties, slim. Their father was 5ft 11in, handsome, compact, but hardly threatening. "And my dad just walks right over to him - Wham! - just smacks him in the face. The guy falls to the ground, blood spurting out of his nose. My dad says a few things to him, gets back in the car, and drives us away."

He remembers the little talk their father had with them. The gist being: You don't have to tell your mother about this. And he remembers looking back at the man as they drove off, now rolling around on the floor, holding his nose, covered with blood. He remembers, mostly, that this was nothing out of the ordinary. "It was so commonplace. That was my father."

Not long after this - maybe a year, maybe less - his father would walk out on them all. It wouldn't be dramatic. He wouldn't leave for a pack of cigarettes, then never return. It would be gradual, piecemeal, and all the worse for that. At first, he just stopped coming back some nights. Then some more nights. Then most nights. Then one day, he just never came back, and ten-year-old Bryan Cranston would not see his father again for almost a decade.

Many years later, when Cranston was 21 and his brother 23, he would decide to track their errant father down - he'd always had an idea where he was. He did it because, like his father, he wanted to be an actor. But more than that, he wanted to know about life.

About fatherhood. About marriage. About what went wrong.

He wanted to know what not to do.

In a way, every story is about fathers and sons. We're all broken or built by our fathers, all seeking approval or railing against them; our moulds bear their thumbprints, especially if they slip. But Bryan Cranston's story is more complicated than most.

Sitting across from GQ for a late breakfast in New York - last night he performed as Lyndon Johnson in his hit Broadway play All The Way, one of the many lifetime ambitions he can now pick off the tree like ripe fruit - he remembers how he first got his head round playing Walter White. To play the cancer-ridden chemistry-teacher-turned-meth-kingpin of Breaking Bad - a role that would see him win four Emmys and a Golden Globe, and be labelled star of the best TV show of all time and given the keys to the Hollywood kingdom, not least this month's Godzilla, he based him on his father.

He gave him his slump, his way of walking, his slouched shoulders, his hunch, his burden: "I gave him the weight of the world."

"Here was a man who was depressed," Cranston says of the early Walter White, before the slow transformation to something much darker in drug lord Heisenberg. "A man much older than his years, who had missed opportunities in life. He loves his family, and gets some joy out of that, but it's all removed."

His father was often out of work. A boxer in his youth - "he was semi-pro, so if there was an altercation, that's how he dealt with it" - and a Navy pilot in the Second World War, he went into acting, appearing in Fifties and Sixties shows like Dragnet and My Three Sons.

But the work was hardly steady and he was hardly a success. One time, says Cranston, they dug out a pool, only to then not be able to afford the chemicals ("My mother just said, no, you can't swim in it"). A new car was swiftly replaced with a beaten-up one. His father imagined various far-fetched money-making schemes, like a trampoline park, or a nightclub with a bowling alley attached. "A typical actor's life. A few bad months, a few good ones. That drove my dad crazy. There was a time he went nuts. He couldn't cope."

The divorce, when it came, split the family apart. It crushed his mother, who tried to feed her family on food stamps. "There was a period where my mother fed us nothing but hot dogs and beans. Or big pots of soup that would stretch weeks. It's not the childhood I would have designed for myself. But it's the one that was destined for me."

Their house was foreclosed on. His sister went to live with their father's mother, Bryan and his brother with their maternal grandmother. His own mother, who also dreamed of acting, became an alcoholic and sunk into depression. She married four more times ("She became like Blanche DuBois"). Both his parents, he says, were "broken" people. "My father wanted to achieve a certain fame. He wanted to achieve stardom. He wanted to have power. And that was a mistake, I think. So I learned from that mistake."

For the longest time, success eluded Cranston Jr too. Unlike his father, however, it did not break him - and unlike his father, he made sure he provided for his family.

If you flicked the TV on in the US in the mid-Eighties, there's a chance you saw one of the greatest actors of his generation extolling the virtues of haemorrhoid cream ("Now you can relieve inflamed haemorrhoidal tissue with the oxygen action of Preparation H") or Coffeemate ("It makes coffee taste creamy, rich, the whole bit!"). There were bit-parts - he played Tim Whatley, a "dentist to the stars" in a few episodes of Seinfeld - but no big breaks. It wasn't until he landed the role of hapless patriarch Hal in family sitcom Malcolm In The Middle in 1999 that he became anything other than a journeyman pro.

He was 43, and married with a young daughter. He had been a professional actor for more than 15 years. He'd never considered quitting.

"No. Look, my greatest achievement is that I've been working as an actor for 25 years. It's about finding the joy in every opportunity to act. If getting the job is the only way to be happy, you'll eventually crash and burn."

Did his father have that joy? "No."

Luck, as it tends to, played a part in Cranston's rise. It was only by playing a racist redneck in a 1998 episode of The X-Files - written by one Vince Gilligan - that, when Gilligan was casting his own show almost a decade later about a meth-cooking chemistry teacher on upstart cable channel AMC, the only person he thought could pull it off was Cranston.

As this was a man, at this point, best known for running around naked covered in 30,000 live bees on Malcolm In The Middle (the writers had a game when devising story lines called "What won't Bryan do?" - it ended without conclusion), it was a tough sell. "Yeah, safe to say there was a fair bit of questioning in the early days," says Gilligan.

Aaron Paul, who plays Jesse Pinkman, Walter's youthful partner in crime, was also unsure at first. But to convince him, the network sent him some DVDs of another show they had just started making: a little workplace drama called Mad Men. "So, I thought, well, they must know what they're doing... but it wasn't until I saw that [The] X-Files episode a couple of years into shooting I realised, wow, this guy [Cranston] has always had this talent. He was just waiting for people to see it."

The scepticism was perhaps understandable. But then, Gilligan was attempting something that, even in the rarefied air of ambitious, sprawling, long-form TV dramas hadn't been done before.

He wanted to take a character, and genuinely change him over the course of a series. As the show's much-parroted mantra has it: "From Mr Chips to Scarface". It would be a rebuttal of that most hackneyed American trope: be the best you can be. The best Walter could be - and the one that finally made him feel most alive - was to become a world-class cook of crystal meth.

The problem was - from the tragic farce of the early Walter, to the ruthless, reptile-eyed drug lord Heisenberg he would become - you needed an actor to pull it off. Could it really be mild-mannered Bryan Cranston? Just where would he dredge that from?

Talk to anyone - his good friend Jason Alexander of Seinfeld fame ("He's the very soul of decency"), his Breaking Bad co-star Aaron Paul ("Just the kindest man I've ever met"), his Godzilla director Gareth Edwards ("The funniest person I've ever met. You leave all conversations feeling bad because you're never going to be as funny"), his Total Recall co-star Colin Farrell ("He's just cool, man. Complete lack of pretence. He's a really unactorly actor... Um, I think I just insulted my whole profession") - and they will say the same thing. In their telling, he may well be the nicest man on the planet.

Certainly, during his breakfast with GQ - he orders eggs benedict, hollandaise on the side, hot sauce on top, the breakfast of champions - you'd have little reason to doubt them. Waitresses are joked with ("The eggs benedict is your favourite too? Well, pull up a chair, join us!"); the odd fan posed with ("A picture?" he says, mid-bite, "Of course!"); when he gets excited, the arms dart out across the table, the hands jab and blur, the air in front of him takes a pounding. If it's an act, he's got excited affability nailed.

And yet, there is another side. Just one he controls very well. One he inherited, he says, from his father. "Yes," he says simply, and quite unexpectedly, "I have an anger thing."

It first became obvious when an ex-girlfriend, a drug-addict, took to stalking him, following him from LA to New York, leaving threatening messages on his machine - "I'm gonna kill you! I'm gonna cut your balls off!" - and eventually showed up at his apartment. He remembers thinking how he would kill her. How he would open the door, grab her by the hair, how he would smash her head into the brick wall, again and again and again, "until her brain matter was dripping down the sides of it... I shuddered and realised how clearly I saw that happening."

Alexander tells me of an incident at a dinner party when Cranston took issue with the host. "Our host was politically inclined a different way than myself and Bryan and he said something like, 'I don't think healthcare is a right; it's a privilege. And Bryan looked him up and down and bellowed, 'What the f*** did you just say?' You could definitely see a shade of what would become Heisenberg."

He began therapy when he realised it was an issue, and has now been going for decades.

"What therapy teaches you is not to deny who you are," he says, "or to try and tell yourself, you know, I shouldn't be angry, I shouldn't be angry. The point is to deal with it, so you have an outlet for it. I hit punching bags, I run. You expel it. And also, reading, thinking, talking about it, it dissipates. I'm able to put my anger into my work. My work is therapy. There are places that you can go on stage and on film that are not acceptable in other areas. I do it every night. I rage at certain things. I get it out."

Cranston is a man forever at war with himself. Each battle is about control - the man he wants to be, and the man he fears to become.

His mother, he says, lived in chaos when his father left. Now, in his house, he labels everything, and wages war on waste and mess.

He tells me a story about looking for sun-dried tomatoes in his fridge and finding only mayonnaise jars that goes on for longer, I would guess, than any celebrity anecdote regarding mayonnaise jars ever has. But the gist is this: he found five, all open, all in various stages of use. "So I reorganised the fridge. The pantry.

And I labelled everything." Now, every single item has its own slot. His wife called him ridiculous. Cranston, however, simply finds it "comforting" - "It relieves the little molecules of stress that add to your day."

He recently designed his own 2,400 sq ft beach house. With a two-car vertical-bay parking garage, the latest high-tech home devices, and rooms with beds that flip down from walls, it's a marvel of economy and design ("I want every square inch to make sense").

He wages war even on the random nature of selecting acting roles, and, by extension, on the chaotic nature of the profession that swallowed both his parents' lives. He has a system for it. He has a chart. He labels it.

Called "Caps" ("It stands for the Cranston Assessment Project Scale"), on the left he writes the offers in blue ballpoint. Along the top, five categories, listed in decreasing order of importance - Story, Script, Role, Director, Cast - each of which he gives a score to. There are bonus points (salary) and minus points (time away from family). And then he decides. Anything under 16, no way.

Anything more than 25, you bet. Argo, directed by Ben Affleck, was a 28. Breaking Bad maxed it out. "Every level was at the top. Easy decision."

Godzilla - the first role he accepted after he finished filming Breaking Bad, and which is in cinemas now - scored highly (20), but not quite highly enough at first, and so he turned it town. His agent convinced him to look at the script again (surprisingly good script - points added!) and he took it. It didn't hurt that it was nothing like Breaking Bad. "That's what ultimately helped. Because it can't be compared.

It's a Godzilla movie! And also, there's a lot of talk about, 'This is the best show ever', and it would be a proud thing to say. But I knew the next thing, if it was a dramatic piece, would have to be that level. People would relate one to the other.

So I didn't want anything next to have to face that mountain."

He even wages war on noise. On Mondays, he simply refuses to speak. "It's my silent day," he says.

And if this means he writes things down when in restaurants ("Like, 'What's the soup?'"), or deal with his wife's concern ("She goes, are you OK?"), then that is the price that Cranston will pay.

Partly, he does this to save his voice, not least when he's on stage. But after a while, he says, "it became a sociological experiment that I enjoy. Because a lot of times, people talk unnecessarily. And if you're busy talking, you're not taking in the art, or the architecture, or the environment you're in. Maybe you don't see the flowers."

Sometimes he has an urge to say something, starts to write it down, then realises, you know what, it's not really worth it. It can wait. And he won't utter a word, because in the battle of Bryan Cranston, he will not be defeated.

He doesn't make a sound.

Everyone agrees that on set Bryan Cranston is the father.

He accepts the role gladly - everything from settling on-set disputes to arranging cast parties. On Breaking Bad, he organised bowling parties. On Total Recall and

Godzilla, he arranged ice-cream trucks. "I gratefully and fully accept that responsibility," he says. "It strengthens the family when you take the time to celebrate moments. And I just wouldn't allow any bullshit." Otherwise, he says, the unit "breaks down".

He became particularly close to Aaron Paul. Tonight, he says with a beaming smile, Paul's coming to see him on Broadway.

There were lots of moments of sadness, fear, in my childhood. So I look on that time and grab what I need "I love him like a son. We'll be friends for life."

Paul will tell me later that he started filming Need For Speed the day after they finished Breaking Bad and a text popped up on his phone from Bryan. It said: "Miss you already." "And it had only been a day!" "He was our father," says Gilligan. "He worked to make the crew and cast feel like a family."

But mainly, adds Gilligan, it wasn't really about the annual end-of-season parties that felt like children's birthdays, or the ice-cream vans that felt like a father's Sunday treat. Mostly, it was something far simpler and yet far more important: Cranston always makes sure he gives the cast and crew his time. "He did it by always being present," he says. "He did it by always being on the set between takes and not in his trailer."

He did it by never leaving them.

It's always tempting to ask what depths an actor plumbs when playing a particularly dark role. With someone like Cranston - a former sitcom clown who went on to play one of the most complicated and fully fleshed antiheroes in TV history - the question is inescapable.

All who've worked with him speak of how non-method he is, how he can switch when someone shouts action. Robert Schenkkan, the Pulitzer-winning playwright of All The Way, marvels at his ability to "turn on a dime" as Lyndon Johnson from a jocular persuader to a "feral-snarling beast"; Gareth Edwards remembers his "gear change, nought to 100 in a split second" on

Godzilla. "He'd do a scene where he'd be crying, then, before I'd said cut, he'd crack a joke and we'd burst out laughing."

But the skill shouldn't be confused with the source, and the craft not confused with the current beneath it.

When Jason Alexander first watched his good friend descend into the depths as Heisenberg on Breaking Bad, he was as surprised as anyone else. But not because of the performance, exactly. Rather, he couldn't spot the acting. "He seemed to just be accomplished by going to a neutral place.

By just turning off that light within him, rather than having to play someone dark, troubled and dangerous. For people who know him, that's what was so startling."

When his father left, Cranston says, the other kids would ask where he was. So he would lie. He would tell them that his dad works late; that they play for hours before his father left for work. But he remembers the pain of it so clearly - and it's a pain he uses to this day. "There were lots of moments of sadness, fear, in my childhood," he says. "So I look back on that time and grab what I need."

He'll decide, "like, I'm going to mix this with this - you know, sorrow, pain, regret. In a way, I'm lucky to have that. There's no block. It's right there. I just let it come out."

And if Cranston's war with himself - if fun, funny, affable, ultra-organised, great-father Bryan is the one he pushes to the surface through sheer force of will, fearing the worst aspects of a nature he has, or maybe just fears he has; if, like Walter White and Heisenberg, he really is two men battling for control of one - then this is where they are most at peace.

"He is an outgoing, happy person," says Gilligan, "and if he's not, if he's not indeed that, then Bryan Cranston is indeed the greatest actor who has ever lived."

Two years before Cranston and his brother went in search of their father, the two of them decided to take off on a road trip.

His brother Kyle, at his side as he had been all those years before in their father's car, was 21, and had just passed his police-cadet exams. He said to Bryan, "All I have to do is pick up my gun and my badge, and I'm officially an Orange Country Sheriff."

Cranston was 19 and, despite preferring acting, was following his brother's lead by taking law enforcement classes at college.

He asked, "Are you gonna do it?"

His brother shook his head. So they got on their motorbikes, and they left. Cranston had $115 in his back pocket.

For two years, they crisscrossed the country. They slept in churches and golf courses, schools and cemeteries; they worked in cafés and carnivals, putting up and tearing down. The Cranston boys were good workers - "They'd say, stay on, stay on" - but they never did. He remembers the homeless mission they stayed at one freezing November in Houston, Texas; he remembers the smell of the men ("I slept with the covers over my head, just going, oh no, oh no..."), how their clothes were taken from them for the night, the pull-chain shower, the tiny cube of soap, the coffee like muddy water, the porridge like paste; he remembers how their clothes came back to them the next day, marinaded in the stench of all the homeless men's rags, and how their own jackets made them dry-retch ("Oh God, I was gagging, you're holding your nose from your own clothes"). But what he remembers mostly is how free they both felt.

He remembers they'd escaped. "We were running away. But we were prudent. I wasn't going to be stuck in something for 20 years like Walter White, thinking, what have I done?"

When they finally did track their father down - when the brothers decided to do it together, not long after their two-year road trip - the first thing he asked him was about acting. "That was my ulterior motive. I wanted to be an actor." But it was also the icebreaker. "It was something we could talk about."

The rest was as you might expect, and maybe some things you don't - the things only fathers and sons know. There was hurt.

There was anger. There was the obvious question of why. "Who are you?" says Cranston. "What happened? What the hell is going on?"

And so they talked - Joe Cranston and his two sons, boys all those years before, sitting in the back of his car afraid; now men. "He was thankful, felt humbled by it," says Cranston. "Because he knew he screwed up."

The epiphany Cranston came away with that day - the lesson he learnt - might not seem like much. It might not seem anything worth writing down, it might seem obvious. But knowing and understanding are two different things. And it's what you do with the realisation that counts. He learnt, he says simply, about mistakes. "And I learnt that you can always make them."

And he learnt what not to do

Godzilla is out now

Originally published in the June 2014 issue of British GQ.