To clarify butter, melt it over low heat without stirring. Once it has melted remove from heat and skim off the solids floating on top.
Place shallots, tarragon, vinegar and wine on medium heat and boil until reduced to about 2 tablespoons of liquid.
Set up a double boiler arrangement with a Pyrex bowl and a saucepan. Place the egg yolks in the bowl and whisk in the reduced vinegar. Place bowl in pan of simmering water and cook, whisking continually, until mixture thickens - about five minutes.
Remove from heat and very slowly whisk in clarified butter. Whisk in salt and pepper to taste.