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1
Combine the white wine vinegar, dry white wine, minced shallots, crushed peppercorns, and chopped tarragon stems in a small saucepan. Bring to a brisk simmer and reduce until only 2 tablespoons of liquid remain. The reduction is done when it is syrupy and intensely concentrated — watery liquid at this stage means weak flavour throughout.
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2
Remove from the heat and allow to cool slightly. Strain the reduction through a fine sieve, pressing the solids; discard the peppercorns and shallot. Transfer the strained liquid to a heatproof bowl.
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3
Whisk the egg yolks into the cooled reduction. Set the bowl over a bain-marie of barely simmering water — the bowl must not touch the water. Whisk continuously over gentle heat, never allowing the temperature to exceed 65 °C. This is where the dish lives or dies: direct heat or excessive temperature will scramble the yolks and no rescue is possible; the mixture is ready when it thickens to a pale, creamy ribbon that holds its trail on the whisk for a moment.
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4
Begin adding the warm clarified butter in drops, whisking constantly. Once the emulsion is clearly established, increase to a thin, steady stream, still whisking without pause. Continue until all 250 g of butter is incorporated. The sauce is thick enough when it coats the back of a spoon heavily and a line drawn through it holds cleanly.
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5
Fold in the chopped fresh tarragon leaves and chopped chervil. Taste: the sauce should read of tarragon, shallot, and butter, with a distinct vinegar backbone. If the consistency is too thick, correct with a few drops of warm water.
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6
Hold the finished sauce over barely warm water at 45–50 °C until service. The sauce is ready to serve when it is warm to the touch but not hot — excessive heat above 60 °C will break the emulsion.