melt the butter
Cut the butter on cubes and add to a saucepan. Place over medium-high heat and let it melt completely. Once bubbles start to form, remove from the heat.
whisk the eggs
Add eggs, egg yolk, and balsamic vinegar (or lemon juice) to a measuring bowl (or in a blender jug). Season with black pepper. Using a blender or an immersion blender, blend until the mixture is pale and fluffy.
Slowly, gradually, pour the hot melted butter in a thin stream into the egg mixture while blending on high speed. When the sauce begins to thicken, you can start pouring the butter in quicker (this will be approx. after you've used half of the hot melted butter). The sauce will be thick, creamy and velvety. Season to taste with salt and cayenne pepper. Serve warm, immediately.