In a small saucepan combine vinegar, wine, shallots and dried tarragon and simmer over moderate heat until reduced to 2 tablespoons of liquid. Cool and strain through a fine sieve.
In the top pan of a double boiler or a heat-proof bowl whisk the egg yolks until they become thick and sticky. Whisk in the reduced vinegar mixture. Place the pan or bowl over simmering, not boiling, water. Whisk until mixture is warm, about 2 minutes. (If mixture appears to become lumpy, dip pan or bowl immediately in a bowl of ice water to cool, whisk until smooth and then continue recipe.) The yolk mixture has thickened enough when you can see the bottom of the pan between strokes and mixture forms a light cream on the wires of the whisk.
Gradually whisk in the melted butter, about 1 tablespoon at a time, thoroughly combining after each addition. As the mixture begins to thicken and become creamy, the butter can be added more rapidly. Do not add the milk solids at the bottom of the melted butter.
Season with fresh tarragon, salt and pepper. Serve immediately. To keep sauce warm set pan or bowl in warm water.