1. Chop enough tarragon leaves to measure 1 tablespoon. In a 2- to 3-quart pan over medium-high heat, bring white wine, vinegar, shallots, peppercorns, and remaining tarragon sprigs to a boil. Cook, stirring often, until liquid is reduced to about 1/3 cup, about 10 minutes. Pour through a fine strainer into a bowl, pressing on solids to extract liquid (discard solids).
2. Meanwhile, in a 1- to 1 1/2-quart pan over low heat, melt all but 2 tablespoons butter; keep warm. In a nonreactive bowl, with a whisk or handheld mixer on high speed, vigorously whisk or beat egg yolks until pale yellow and thick, about 5 minutes by hand. Add 3 tablespoons white-wine mixture; whisk or beat to combine. Add remaining 2 tablespoons solid butter. Nest bowl over a 3- to 4-quart pan of barely simmering water (bottom of bowl shouldn't touch water). Whisk vigorously or beat until butter has melted and mixture has emulsified and thickened, about 3 minutes. Remove from over water.
3. Whisking or beating constantly, pour in warm melted butter in a very thin, even stream; sauce should become smooth and emulsified (see notes). Continue whisking or beating until all butter is incorporated and sauce is creamy, 5 to 7 minutes. Add chopped tarragon and hot sauce; taste and add more wine mixture, more hot sauce, and salt if desired. If sauce is too cool for your liking, set bowl back over hot water and whisk just until warm to touch, no longer than 2 minutes. Serve at once.
Nutritional analysis per tablespoon.