Place the shallots, wine and tarragon vinegar into a non-reactive saucepan. Reduce the liquid, over a very low flame until the liquid is less than 1/2 of its original volume (about 3 Tbl). Remove the pan from heat. Allow this reduction to cool to room temperature. If desired, strain the shallots off the reduction.
Break the eggs and separate the whites from the yokes. Make sure that the clarified butter is warm, but not scaldingly hot. In a sauteuse over a very low flame, throw the wine/vinegar reduction into the pan. Add the egg yokes, whisking them constantly until they achieve a ribbon-like consistency. (If it appears that the heat is increasing too fast, move the pan off the burner to prevent the eggs from scrambling.) Add the clarified butter - drizzling a ladle at a time and whisking until the sauce comes together. The sauce should resemble the texture of mayonaise. Sprinkle in the cayenne and salt and pepper to taste. Cut off the heat. Keep this sauce warm. If reheated, it will break.