Combine the shallots, tarragon and vinegar in a saucepan over medium heat. Simmer for about 5 minutes until just 1 tablespoon of liquid remains. Strain and reserve the liquid.
Combine the egg yolks, reduced vinegar, lemon juice and salt in a blender or food processor. Blend well till combined. Slowly pour in a stream of the hot melted butter while blending until all butter is incorporated.
Serve the sauce in a sauce boat with extra chopped tarragon on top, or drizzled over your favourite dish.