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1
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Combine vinegar, wine, shallots, black pepper, and 1 1/2 teaspoons tarragon in a small saucepan.
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Cook over medium heat until reduced to 1 tablespoon, 5 to 10 minutes.
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Add egg yolks and 1 tablespoon of water to reduced vinegar mixture.
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Whisk until thick and pale, about 2 minutes.
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Set pan over moderately low heat and continue to whisk at reasonable speed reaching all over bottom and insides of pan, where eggs tend to overcook.
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To moderate heat, frequently move pan off burner for a few seconds, then back on.
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7
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As they cook, the eggs will become frothy and increase in volume, then thicken.
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8
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When the bottom of the pan is visible in the streaks left by the whisk and the eggs are thick and smooth, remove from heat.
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9
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By spoonfuls, add soft butter, whisking constantly to incorporate each addition.
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10
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As the emulsion forms, add butter in slightly larger amounts, always whisking until fully absorbed.
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Continue incorporating butter until sauce has thickened to consistency desired.
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Season with salt, remaining 1 1/2 teaspoons chopped tarragon and, if desired, pepper.
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Add a few droplets of lemon juice if necessary.
