In a small saucepan, combine the tarragon, shallots, vinegar, and wine. Bring to a simmer over medium-high heat and cook until reduced by half, about 10 minutes. Remove from the heat and set aside.
Set a stainless steel bowl over a saucepan of simmering water, or use a double boiler. Add the egg yolks and whisk until doubled in volume. Slowly add the melted butter, beating constantly to prevent the eggs from scrambling, until the sauce is thickened, 10 to 12 minutes. Stir in the shallot mixture and season with salt and pepper. Keep warm until ready to serve.
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