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 of double boiler or a heat-proof bowl whisk the egg yolks until they become thick and sticky. Whisk in the reduced vinegar mixture and pepper. Place the pan or bowl over a saucepan of simmering, not boiling, water. Whisk until mixture is warm, about 2 minutes. (If mixture appears to become lumpy, dip pan 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 whip.
While whisking the yolk mixture gradually pour in the melted butter, a tablespoon or so at a time whisking thoroughly to incorporate before adding more butter. 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 the sauce to taste with chopped tarragon, salt and pepper. To keep the sauce warm, set the pan or bowl in lukewarm water or in a thermos.