Use this sauce with grilled or sauteed meat. It is quite a rich sauce, so don't plan too hearty a menu to serve with it.
Simmer the shallots in vinegar and white wine until liquid has been reduced by about two thirds. Remove from heat and cool.
Place this mixture in blender and add egg yolks, tarragon, peppercorns, salt, and dry mustard. Blend at high speed for no more than 10 seconds.
Add the warm, melted butter, cayenne, and a squeeze of lemon juice (optional). Quickly turn on blender again and let it rotate until sauce thickens. Should it become too thick, add a bit of hot water and blend again.