In a medium saute pan, combine the shallots, pepper, 2 tablespoons of the tarragon, vinegar, and wine over medium high heat.
Cook until reduced to about 3 tablespoons.
Add the water, stir, and remove from heat.
Cool for about 15 minutes in a measuring cup.
Combine the reduction, the egg yolks and 1 teaspoon of salt in a blender.
Blend for about 30 seconds.
With the blender on, slowly pour the melted butter through the lid of the blender.
Add the remaining 2 tablespoons of tarragon and blend for just a few seconds.
If the sauce is too thick, add a little more wine.
Keep at room temp until ready to serve.