In a small saucepan over low heat, melt the butter until bubbling hot. In a blender, add the vinegar and egg yolks and blend on high speed for several seconds. With the blender still running, remove the center lid of the blender. Pour the hot butter in a thin, steady stream into the whirling egg mixture. Add the tarragon and shallot and continue to blend. Add salt and pepper to taste.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.