I embark upon this column in the full and certain knowledge that many of you already know how to fry an egg. Indeed, if you are completely confident in your abilities, and never find yourself disappointed by a sadly snotty white or tragically chalky yolk, then pat yourself on the back and then move along – I can teach you nothing. But if, like me, you can fry a perfectly decent egg but wouldn't stake your life on your habitual method, then you are more than welcome to join this brave voyage back to the basics of cookery.

Those still reading should take heart from the fact that the great Fernand Point, feted as the father of modern French cuisine, is said to have judged a chef by the way he fried eggs. He'd interrupt hopeful apprentices at the stove, legends including Paul Bocuse and the Troisgros brothers, with the cry, "Stop, unhappy man – you are making a dog's breakfast of it!" before demonstrating the only proper way to execute the dish.

Further reassurance comes from award winning Spanish chef José Andrés, who claims "my whole life I have been trying to cook an egg in the right way." Andrés exalts in what he calls "the humbleness" of the dish, but that doesn't mean he just slings it into a hot pan and goes off to make some toast – far from it. Both these culinary giants have very different ways of frying an egg – but who's right? (Note here I'm aiming for the standard British fried egg, known in the States (and perhaps elsewhere?) as "sunny-side up". There will be no flipping.)

The egg itself: when is an oeuf an oeuf?

Here I'll be concentrating on the hen's egg because, realistically, that's what most of us cook up, but it's worth pointing out that duck eggs have larger yolks, proportionally (and are also bigger all round) and, arguably, a better flavour than many commercial hen's eggs. Be aware, however, that the higher protein content of the white will mean it cooks through more quickly, so it may take some practice to get right. (With ostrich eggs, you're on your own.)

As ever, if you keep your eggs in the fridge, then you should let them come to room temperature before cooking – if you start with a cold egg, then you're more likely to end up overcooking the yolk trying to get the white to set. Very fresh eggs are best for frying, because the stronger proteins will give you a neater shape (this may sound obvious, but older eggs are better for things like boiling, because they're easier to peel).

The cooking fat

Delia Smith recipe fried egg. Photograph: Felicity Cloake

Frying obviously involves adding fat – that's why it's so popular. Bacon fat is the traditional choice in this country, and still advocated by Delia, but very few of us eat enough of the stuff to have any around: I often use it if I'm doing eggs and bacon for breakfast, but although the flavour's good, it does make for a messy looking egg. Delia also suggests substituting groundnut oil, which creates the opposite problem – it's clean, certainly, but deliberately neutral tastewise.

More popular are olive oil, as favoured by Jamie Oliver, the aforementioned Andrés, and American food writer David Rosengarten ("the unaccustomed marriage of fruity olive oil flavor with creamy egg defines anew the upper limits of fried-egg excitement"), and butter, beloved of Point, his culinary disciple Bernard Loiseau, and Cook's Illustrated, among others.

Both lend their distinctive flavours to the egg, so it depends what you're going to be serving the dish with – I'd default to butter, because I think the richness is a better complement for the yolk, but if I were plopping it on top of a pile of morcilla and chickpeas, I might go for olive oil instead. (For a fry up, however, I will brook naught but butter.)

The cooking temperature

José Andrés recipe fried egg. Photograph: Felicity Cloake

Delia uses a high heat for her favourite fried egg, which, she explains, has a "slightly crispy, frilly edge; the white will be set and the yolk soft and runny". She cooks it at this temperature for 30 seconds, then turns the heat down to medium for another minute, which does indeed yield the crisp white she describes. I find it too tough for my taste though: it's like chewing through a hairball, although I concede that the yolk itself is satisfyingly runny.

Andrés goes for a medium-high heat instead and, like Delia, tilts the pan to baste the egg throughout cooking. Using a smaller, steep-sided sauté pan and more oil, however, means his egg sits in a pool of hot fat, almost as if it's being shallow fried. It takes me a few goes, and a lot of spitting oil, to get the technique right, but it yields a perfectly cooked egg in just 30 seconds – if you don't mind it looking like a brown poached egg rather than a cheery fried one. Andrés explains that the technique "achieves a higher level of browning around the entire surface of the white, which imparts a distinctive, much more flavourful taste, given the level of caramelisation of the proteins and sugars". Personally, although the contrast of texture between this outer shell and the soft, gooey yolk inside is undoubtedly interesting, it's not what I want on my breakfast plate.

Jamie Oliver recipe fried egg. Photograph: Felicity Cloake

Oliver dismisses such "crispy, bubbly eggs" in favour of cooking them gently over a medium-low heat. Indeed, he suggests cracking the egg into a cool pan, and allowing it to heat with the oil, cautioning that "if [it] starts to spit ... turn the heat right down". Far better from a cleaning point of view, certainly, but is the result noticeably nicer? It's certainly "soft and silky" as promised, but the white takes absolutely ages to cook through. They're the best eggs yet, but I'm not convinced they're perfect.

Fernand Point recipe fried egg. Photograph: Felicity Cloake

Point cooks his egg on a heat "so low that the white barely turns creamy", and then finishes it off with melted butter. This is certainly a nice idea, but apart from the fact it's more butter than egg (an idea not without its attractions, I admit), it leaves me with quite a lot of undercooked white. I assume this is a deficiency in the iteration of the recipe, rather than Point's technique, but a lump of melted butter is never going to cook a white that's not even changed colour properly.

Tricks of the trade

Cook's Illustrated recipe fried egg. Photograph: Felicity Cloake

Cook's Illustrated stresses that the egg should be fried "over the lowest possible heat", but, unlike Point, the butter is allowed to foam rather than simply melt. They then cover the pan for the duration of the cooking to help speed up the process, which results in an almost perfectly cooked egg – a soft, but firm white, and a gorgeously runny yolk.

Lucinda Scala Quinn recipe fried egg. Photograph: Felicity Cloake

Martha Stewart's "executive food director" Lucinda Scala Quinn's perfect egg recipe is similar, but she adds a teaspoon of water to the pan to help steam the egg. I don't think this is necessary: the Cook's Illustrated egg is just as well cooked and has a better flavour without the dilution of the butter.

Bernard Loiseau recipe fried egg. Photograph: Felicity Cloake

Loiseau takes Point's low-heat technique a step further by cooking his egg on a saucer set over a pan of simmering water and then basting it with hot butter as before. It's even softer, but I'm beginning to wonder whether this is an entirely desirable quality – on reflection, I'd quite like my egg white to have some bite to it.

David Rosengarten recipe fried egg. Photograph: Felicity Cloake

Step forward David Rosengarten, who deep fries in olive oil for what he claims is "the crispiest, most flavorful fried eggs of all". He stresses the importance of sliding a spatula under the egg within 10 seconds of it entering the oil, a lesson I learn the hard way as I struggle to detach a monstrously overcooked egg from the pan, but otherwise, the technique is fairly simple. The results, however, are not for me – although the yolk is perfectly cooked, the white is almost crunchy, and very greasy. And as for the cleaning up ...

Lastly, and with some trepidation, I try the sous-vide technique from Dr Nathan Myrhvold's new Modernist Cuisine at Home, a book apparently "destined to set a new standard for home cookbooks". It certainly sets a new standard for fried eggs: to make his sunny-side up eggs, I first need to borrow a sous vide machine from Lakeland.

Dr Nathan Myrhvold recipe modernist sous vide 'fried' egg. Photograph: Felicity Cloake

Myrhvold explains that cooking the perfect fried egg poses an inherent problem as the yolks and whites reach their ideal states at different temperatures. To counter this, he cooks whole eggs in a 67C water bath for 40 minutes, until the yolks are "jammy", and discards the soupy whites. Ten fresh whites (for 4 yolks!) are whisked together with double cream and salt, and then baked, covered, in an 160C oven for 12 minutes. Once they're just set, the yolks are plopped on top and it's ready to serve, a mere one-and-a-quarter hours after I started. Despite my scepticism, it's all delicious: the whites tender and creamy, the yolks sticky and rich (although I wish I'd noticed his instruction to cook the yolks at 62C for the runny centres I like) – but it doesn't taste like a fried egg, for all my efforts. More a dinner party dish than a breakfast staple.

In an attempt to simplify the process, I also try separating the eggs and then frying them as normal, adding the yolks a minute into cooking, but it's a fiddly business (relatively speaking) and I don't think the results are any better than the covered eggs I liked so much. So I'll be sticking with this simple but effective method – quick and easy enough to make the morning after the night before, and guaranteed to hit the spot every time.

Perfect fried eggs

Felicity's perfect fried egg. Photograph: Felicity Cloake

For each egg

1 fresh egg, at room temperature

1 tbsp butter

Salt and pepper

Place a saucepan lid over the cooking eggs. Photograph: Felicity Cloake

1. Crack the egg on to a saucer to make it easier to slide into the pan. Heat the butter in a heavy-based frying pan over a low heat, and find a slightly domed saucepan lid, ideally slightly smaller than the pan itself, so you can place it over the cooking eggs.

2. Once the butter has melted, but not begun to foam, swirl it around the pan to coat, then slide in the egg. If you're cooking more than one, be careful not to crowd the pan. 3. Cover and leave for 3½ minutes, then check the white is cooked, lift out, season gently, and serve immediately

Fried eggs: the cornerstone of a good breakfast, or the fallback option for those who haven't mastered scrambled or poached? How do you cook your perfect fried egg, and what else do you serve them with apart from a hearty fry up?