Crack the eggs carefully and separate the yolks from the whites, placing the bright yellow yolks into a heat-proof bowl. You can set the whites aside in the refrigerator to use later for a high-protein omelet.
Cut the unsalted butter into small cubes and heat it in a saucepan until it is completely melted and bubbling slightly. Ensure the butter is hot but not browned, as this heat is necessary to properly thicken the sauce.
Place the bowl of yolks over a saucepan of gently simmering water to create a double boiler. Add the fresh lemon juice and salt, whisking constantly until the mixture becomes frothy and lightens in color.
Remove the bowl from the heat and begin pouring the hot butter in a very thin, slow stream while whisking vigorously. This slow addition is the key to creating a stable, heavy emulsion that won’t separate into a greasy mess.
Once all the butter is incorporated and the sauce is thick enough to coat a spoon, stir in a pinch of cayenne pepper. Serve this rich glaze immediately over your favorite high-protein vegetarian dishes.