This is one of the great French classics of butter-based sauces.
Take all the sauce ingredients out of the fridge in good time. The temperature differences should be as small as possible - it's crucial for the success of your sauce.
Use a heavy-bottomed pot and clarify the butter over low heat.
Remove from the heat and pour the butter into a pitcher or measuring cup. Let it settle and remove the whey (the white foam) with a spoon. It's okay if you don't get all the whey out.
Let the butter cool to room temperature - this usually takes about 20 minutes.
Take another heavy-bottomed pot and turn on the lowest heat on the stove.
Whisk the white wine with egg yolks and lemon juice in the pot. This can be done over a water bath, as it's easier to manage (but it's not necessary).
Continue until the mixture has reached a good thickness, similar to eggnog.
Slowly add a bit of butter while whisking vigorously. The sauce will gradually thicken.
Season to taste with salt, pepper, and possibly more lemon juice.
The sauce can be kept warm over a water bath if it’s not served immediately - but make sure it doesn't get too hot. Similarly, the sauce will separate if it gets too cold and you continue to stir it.