Hollandaise variations include bearnaise sauce, which is flavored with a reduction of shallots, white wine, vinegar, and tarragon.
Place the white wine, white-wine vinegar, shallots, 2 tablespoons tarragon, and the peppercorns in a small saucepan set over medium-high heat. Bring mixture to a boil, and cook until it is reduced to about 2 tablespoons.
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 wine mixture and salt, and whisk until well combined. Gradually add 1/4 cup boiling water, whisking constantly. Place bowl over the medium saucepan of boiling water; reduce heat to lowest setting. Whisking constantly, cook until whisk leaves a trail in the mixture and sauce 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 added about a tablespoon of the melted butter, you can begin to add it slightly faster, still whisking constantly. Still, be careful: If the butter is added too quickly, the emulsion will be too thin or will "break" (separate).
Once all of the butter has been added, adjust the seasoning with the lemon juice, and stir in the remaining tarragon. If the bearnaise becomes too thick, you may thin it with a little additional lemon juice or water. If not serving immediately, place pan of sauce over a pot of simmering water that has been removed from heat, or in a warm spot on the stove for up to 1 hour. Alternatively, you may store for up to 3 hours in a clean thermos that has been warmed with hot but not boiling water.