Combine Ingredients - Place egg yolks, water, and vinegar in a medium stainless steel bowl. Set aside.
Heat the Water - Fill a saucepan with about 2 inches of water. The bottom of the bowl containing the egg mixture should not touch the water. Bring the water to a simmer over medium heat.
Whisk the Eggs - Place the bowl on top of the saucepan. Whisk the mixture vigorously and continuously until the eggs turn cream-colored and thickened, about 3 minutes. Remove the bowl from the pot. Whisk in the lemon juice to help the egg stop cooking.
Melt the Butter - Melt the butter in a medium skillet over low heat. It should be warmed to between 140 to 145ºF (60 to 63ºC) when added to the egg yolk mixture.
Add the Butter to the Eggs - Nestle the bowl containing the egg mixture in a kitchen towel to keep it in place when whisking. Add a few drops of melted butter into the eggs very slowly, constantly whisking to create an emulsion.Gradually add more butter, constantly whisking until all of it is incorporated. The sauce should be thick and velvety.
Season the Sauce - Add in salt and cayenne pepper to taste. Add more lemon juice if desired for a more tartness.