Jon Hamm and I are at lunch to discuss his latest movie, Baby Driver, from the director Edgar Wright. But, of course, we’re talking about Don Draper instead, the existential ad man that Hamm immortalised in Mad Men. Jones in West Hollywood is a very Mad Men restaurant. It’s a low-lit, red-leather booth spot that has seen plenty of three- martini lunches in its day. But it’s steak salad and sparkling water today.

“You remember the falling man?” he says. He means the opening credits where an animated Draper falls through the air. “He falls and falls and then lands on the couch sitting perfectly. That’s Don’s journey. Straight down and then pulling up at the bottom.”

I know in England you say ‘therapy’ and people are like, ‘Woah, are you OK?’ But here it’s like going to the dentist

As Draper, Hamm’s journey lacked that perfect finish. It was a swooping ascent from obscurity to stardom but, in the final season of Mad Men, as his career was peaking, his life-changing role came to an end, he split up with his partner of 18 years (the actor and director Jennifer Westfeldt) and he went to rehab for drinking. It looked like things were unravelling. That his success might even be a little bittersweet.

“I can see why people would think that,” he says, brow furrowed. “But it’s not dominoes falling. It’s one chapter closing and another beginning, and as hard as it is to go through, it’s ultimately healthy and necessary.”

Not a midlife crisis then?

“No, but a major shift. Getting famous, coming off a regular schedule on a show, coming out of a long-term relationship, getting older. It’s a rearrangement of stuff that was in a specific order before. And that takes some getting used to.”

Clean getaway: John Hamm in Baby Driver with fellow robbers (from left) Eiza González, Ansel Elgort and Jamie Foxx. Photograph: Wilson Webb/TriStar Pictures

He looks bigger than he does on TV – 6ft 2in and 200lb, square shouldered and square jawed. Handsome, but in a weary, unshaven way, as though life sits heavily on the shoulders sometimes, handsome or not. And it’s a look that serves him well in Baby Driver, a blast of a movie, in which he plays Buddy, a Wall Street type whose midlife crisis has led him to join a gang of robbers led by Kevin Spacey.

“I saw him as a handsome thief in that tradition of Steve McQueen in The Getaway, or George Clooney in Out of Sight,” says Wright, “but with a much darker undercurrent.” He wrote Buddy with Hamm in mind. They’ve been friends for years, ever since meeting at an afterparty for Saturday Night Live, when Hamm hosted in 2008. Practically neighbours in Los Feliz in LA, they’d go for drinks at a local restaurant called Little Dom’s. “I just gave Edgar a ring: ‘Hey you want to grab a drink?’” says Hamm. “Because if you’re not working in LA, you’re not doing anything.”

But Buddy is only a supporting role – Ansel Elgort is the driver of the title. This has largely been the way with Hamm’s movie career, from Bridesmaids and The Town, up to Absolutely Fabulous and Keeping Up with the Joneses, and he is fine with it. “Sure, it’d be fun to do a big franchise movie, or another prestige TV series, but mostly I just gravitate towards people whose work I find… non-traditional,” he says. People like Wright, or Charlie Brooker – he’s appeared in the TV show Black Mirror.

Wright wrote Buddy as a character with a dark side. He starts off as Elgort’s ally, but ends up trying to kill him. “That’s what Matthew Weiner [the creator of Mad Men] saw in Jon, too,” he says, “a handsome, strong male with secrets.”

The dapper don: as Don Draper in Mad Men. “I’m happy I was good in it. Nobody wants to be like the worst guy on the field. Oh God, don’t pass to him…’ Photograph: Allstar

In person, though, Hamm’s not especially secretive. He’s happy to talk about the therapy he went through after Mad Men, for instance. “I know in England you say ‘therapy’ and people are like, ‘Woah, are you OK?’ But here it’s like going to the dentist. If you can afford it, why wouldn’t you?” (Hamm can afford it. “I’m not set for life, but I’m not scrambling either.”)

He learned the importance of structure, a morning routine and schedule. “I used to have six to eight months of every year all planned out, and then it evaporated,” he says. “Some people immediately build the scaffolding back up, but I’m more subject to inertia – a day turns into a week turns into a month and then you can’t see the shore any more.”

No need to self-flagellate and say: ‘I don’t deserve this.’ Just enjoy the success

You can hear the therapy in the way he talks. He wants to avoid “patterns that are repetitive and destructive” and instead choose “inspiration and creativity”. And this involves “engaging with life”, which is trickier for Hamm than for most. Even just coming to the restaurant today from a photo studio five minutes’ walk away, he chose to drive rather than walk past a building site.

“It’s weird that that’s the reward: ‘Oh you did a great job at something, so we’re going to hound you in public so that you feel every move you make is watched,’” he says, only partly amused. “Going through that for the first time at 35 was like: ‘Woah!’ Now I can clock if I’m being photographed from across the street. I just try not to pick my nose.”

For a while he rants amicably about the internet, the iPhone and how everything is online forever these days with social media, in which he doesn’t participate. But soon the vague therapese resurfaces. Like Don Draper who has something of a spiritual awakening at the end of Mad Men, Hamm also speaks of a Zen approach to life and enjoying “the now”. “Don’t worry about what happened a year ago, or what movie I’m going to get next. Actors get wrapped up in all that and miss that it’s a beautiful day outside. My focus is on being present. Be here now. Which is a great album actually.”

So no plan?

“Well I’m not a rudderless skiff, but I don’t waste energy worrying about it. I have so little energy as it is.” He grins. “I’m a big nap guy.”

Comic timing: in Unbreakable Kimmy Schmidt with Ellie Kemper. Photograph: Eric Liebowitz/Netflix

One can’t begrudge Hamm a nap after the road he’s travelled. The legend of Hamm is a heartening story.

Born in St Louis to a secretary mother and a father who ran a trucking business, he was two when they divorced, 10 when his mother died of cancer and by 20, he’d lost his father and grandmother, too, who had played a significant role in raising him. “That’s what’s bittersweet about my success,” he says. “My parents never got to see it.”

For two years, he lived in his college roommate’s parents’ house, in the basement, eventually finding a job as a high-school drama teacher. Then after a year of that, he decided to give Hollywood a try, moving in with an aunt in Silverlake. If it didn’t work out in five years, he told himself, he could always come back and teach.

For years, he got nowhere. “Paul Rudd was my one contact, and he was a big deal already – he was off to do Baz Luhrmann’s Romeo and Juliet. So I said: ‘Look, I’m only going to ask one thing and that’s it – just give me a number to call.” That led to Hamm’s first manager, who led to his agent at William Morris, and then three years of auditions without a single bite. Then he lost his agent. It was around this time he worked as a set dresser on a porn film, in between waiting tables. And look how things came around. “I worked at a restaurant downtown where the parking lot we used became the studio where we shot Mad Men.”

Before the split: with partner of 18 years Jennifer Westfeldt. ‘It’s a rearrangement of stuff that was in a specific order before. And that takes some getting used to.’ Photograph: Jon Kopaloff/FilmMagic

There were tough years. Despondent. “Watching other people succeed while you’re stuck is hard,” he says. But his persistence paid off. He went from his first credit on Ally McBeal as “Gorgeous Guy at the bar” to a TV series, Providence, which afforded him his first house in Los Feliz, where he lived with Westfeldt. They hung out with a comedy crowd back then – David Cross, Jack Black, Patton Oswalt. Hamm has been a comedy guy ever since. Tonight, in fact, he’s off to do some improv for some friends.

“Jon’s comedy chops are not in question,” Wright says. “He’s very dry, very quick. When he hosted SNL, Lorne Michaels [the producer] took to him immediately and Jon did 30 Rock, The Unbreakable Kimmy Schmidt… It’s rare to find a dramatic actor who’s also funny. Handsome people aren’t usually funny either.”

When I put this to Hamm, though, he bristles. “That’s certainly not been my experience. Kristen Wiig is a beautiful lady and she’s one of the funniest people I know. And Tina Fey, Amy Poehler…”

And men?

“OK, well, Aziz Ansari is a handsome man.”

Aziz Ansari?

“Yeah. And Tom Cruise is really funny. And George Clooney, Matt Damon…”

Hamm has the model’s burden. “I bring more to the table than what I represent physically,” he says. “And it’s a daily struggle to prove that. Obviously it’s a lovely thing for people to say… [I’m handsome], but sometimes it comes with a shitty dig underneath.”

At 36, he became a byword for a kind of unapologetic masculinity, a pre-feminist philanderer with a tumbler of liquor in his hand. He was invited to the White House to meet Obama and rub shoulders with Jay Z. And as a late bloomer – even later than George Clooney, though Bill Nighy has him beat – Hamm surfed the wave without losing himself. As Wright says: “Actors who find success late are often very grateful. It adds to Jon’s wry take on life.”

“As crazy and superficial as it is, success can be pretty fun. No need to self-flagellate and say: ‘I don’t deserve this’, or ‘It’s all bullshit.’ A lot of Midwesterners and Brits, too, have this false modesty thing. Just enjoy it. It’s ephemeral, like everything in this business.”

What’s more durable, however, is the impact of Mad Men, which makes him quietly proud. “It’s a moment people will remember. And I was happy that I was good in it. Nobody wants to be like the worst guy on the field. Oh God, don’t pass to him…”

But he checks himself. “I’m not resting on my laurels, I prove myself every day…” And we’re back to living in the now. Embracing the present.

There are films in the pipeline – a thriller with Rosamund Pike, a drama with Catherine Keener – and a couple of others on the boil, “but I don’t spend every waking hour trying to wrestle them into existence.” He has no plans to direct having directed a couple of episodes of Mad Men – “I know what it takes.” And he doesn’t pine for the dizzy heights of Mad Men either, though he suspects that that kind of cultural impact is the domain of television more than movies these days. “The age of the indelible movie performance, like The Godfather, is in recession. But it’ll be back. Even pleated trousers are coming back.”

Jon Hamm photographed for the Observer Magazine on the 6 June in LA. Opening picture: Jon wears jacket and trousers by H&M; T-shirt by Alternative Apparel. This picture: jumper by Ermenegildo Zegna. Styling Lawren Sample. Grooming Kim Verbeck. Photograph: Patrick Fraser/The Observer

Starting out, Hamm never dreamed he’d become a Tom Cruise-style action star, but more of a Jeff Bridges, one of the few people that have left him star struck. “I met him after he won his Oscar for True Grit, and just babbled incoherently and walked away. In work and in life, Jeff’s done it right.”

With thoughts of the Dude in mind, we crack open our fortune cookies, and hold the little messages up to read. He raises an eyebrow. “Mine just says: ‘Stop talking.’”

Baby Driver is released on 28 June

