In a small saucepan, combine the vinegar, wine, shallot, tarragon sprigs and pepper; bring to a boil. Reduce heat; simmer for 10 minutes or until mixture is reduced by half. Strain and set liquid aside; discard solids.
In a small heavy saucepan, whisk the egg yolks, water, salt, white pepper and reserved vinegar liquid. Cook and stir over low heat until the mixture begins to thicken, bubbles around the edges and reaches 160°. Gradually whisk in butter. Remove from the heat; stir in minced tarragon and parsley. Serve immediately.