Combine wine, vermouth, shallot and tarragon in small saucepan. Boil down to half of the original quantity (approximately 1/4 cup should remain). Strain. Put egg yolks in cold double boiler. Water in double boiler should not touch bottom of upper pan. Beat with flat bottomed whisk until they look creamy and lemony. Over medium heat, slowly add melted butter while continuously stirring. When all butter has been added, immediately add strained tarragon mixture (do not overcook once butter has been added). Adding tarragon mixture will make the sauce very thin. Continue stirring and cooking over medium to low heat until sauce starts to thicken. Do not let sauce get too thick; it will continue to thicken once removed from heat. Add a few shakes of white pepper to taste. Remove from heat immediately.