For the sauce, put the white vinegar, white wine, shallots, 1 tablespoon tarragon leaves, ¼ teaspoon salt, and ¼ teaspoon pepper in the 2 Quart Saucepan.
Bring to a boil and simmer over medium heat for about 5 minutes, until the mixture is reduced to a few tablespoons.
Cool slightly.
Place the cooled mixture with the egg yolks and 1 teaspoon salt in the jar of a blender and blend for 30 seconds.
With blender on, slowly pour the hot butter through the opening in the lid.
Add the remaining 2 tablespoons of tarragon leaves and blend only for a second.
If the sauce is too thick, add a tablespoon of white wine to thin.
Keep at room temperature until serving.
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