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1
Combine the shallot brunoise, cracked white peppercorns, tarragon stems, white wine vinegar, and dry white wine in a small saucepan. Bring to a simmer over medium heat and reduce until only two tablespoons of thick, fragrant liquid remain. Strain through a fine sieve, pressing the solids, and allow to cool slightly. The reduction is ready when it is dense and strongly aromatic — thin or pallid liquid is insufficient.
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2
Transfer the strained reduction to a heatproof bowl. Add the egg yolks and set the bowl over a bain-marie held strictly between 55 °C and 62 °C. Whisk constantly. This is where the dish lives or dies: below 55 °C the yolks will not thicken; above 65 °C they scramble into an irreversible curdle. The mixture is ready when it falls from the whisk in thick, ribbon-like folds that hold their shape briefly on the surface.
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3
Remove the bowl from the bain-marie. Begin adding the warm clarified butter in the thinnest possible stream, whisking without pause. Do not rush the addition. The sauce is ready when it reaches a thick, spoonable consistency that holds its shape on a spoon and does not immediately run.
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4
Taste the sauce. It must assert tarragon and vinegar clearly, with rich butter in the background. If the sauce tastes primarily of butter, the reduction was too dilute and the balance cannot be corrected at this stage. A gentle warmth from the white pepper should be perceptible on the finish.
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5
Fold in the reserved tarragon leaves, cut to a fine chiffonade, and the pinch of chervil. Serve immediately. Béarnaise tolerates no reheating and will thin and eventually break if held on the bain-marie beyond 20–30 minutes. It is made à la minute.