Gather the ingredients.
Combine vinegar, white wine, shallots, 1 tablespoon chopped tarragon, 1/4 teaspoon salt, and the black pepper in a small saucepan.
Bring to a boil and simmer over medium heat for 5 minutes until mixture is reduced to a few tablespoons. Cool slightly.
Transfer cooled mixture with egg yolks and 1 teaspoon salt into a blender. Blend 30 seconds.
With blender on, slowly pour hot butter through opening in lid. Add remaining 1 tablespoon tarragon leaves and blend for only a second.
If the sauce is too thick, add a tablespoon of white wine to thin.