Melt the butter in a small saucepan over medium-low heat. Keep warm until ready to use.

Place egg yolks in a copper or stainless-steel bowl that fits snugly in the top of a medium saucepan. Fill the saucepan with 2 inches of water, and bring to a boil. Whisk the yolks, off the heat, until they become pale. Add 1 tablespoon of lemon juice and the salt, and whisk until well combined. Gradually add 1/4 cup boiling water, whisking constantly. Place bowl over medium saucepan containing boiling water, and reduce heat to lowest setting. Whisking constantly, cook until the whisk leaves a trail in the mixture and it begins to hold its shape. Remove from heat.

Pour the warm melted butter into a glass measuring cup. Add to yolk mixture, one drop at a time, whisking constantly. After you have used about a tablespoon of the melted butter, you can start adding it slightly faster, still whisking constantly. If the butter is added too quickly, the emulsion will be too thin or will "break."

Once all of the butter has been added, adjust the seasoning with the remaining tablespoon lemon juice and cayenne pepper. If the sauce is too thick, you may thin it with a little additional lemon juice or water. If not serving immediately, place over a pot of simmering water removed from heat, or in a warm spot on the stove up to 1 hour. Alternatively, store in a clean thermos that has been warmed with hot but not boiling water for up to 3 hours.