Get a saucepan and a heatproof mixing bowl that will sit stably over the pan. Half-fill the pan with water and bring to a simmer. Turn down the heat as low as it can go but still have the water simmering.
Place the butter in a medium pan over a low heat, so it starts to melt but doesn’t burn. When the butter has melted, take it off the heat.
Place the egg yolks in your heatproof mixing bowl, which you should then place over the pan of just-simmering water. It’s important that the saucepan is on a low heat, or the eggs will scramble.
Using a balloon whisk, start to beat your eggs, then whisk in your white wine vinegar.
Keep whisking, and then start adding the melted butter by slowly drizzling it in, whisking all the time, till all the butter has been incorporated. The result should be a lovely, smooth, thick sauce.
Season carefully with sea salt and black pepper, and loosen if necessary with little squeezes of lemon juice. Keep tasting the sauce until the flavour is to your liking.