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1
Combine the white wine vinegar, dry white wine, chopped mint stems, crushed peppercorns, and minced shallot in a small saucepan. Bring to a simmer over medium heat and reduce by three-quarters until the pan is nearly dry. The reduction is ready when only a few tablespoons of deeply concentrated, fragrant liquid remain.
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2
Strain the reduction through a fine sieve, pressing the solids to extract all liquid. Discard the solids. Allow the strained reduction to cool until warm but no longer steaming — it must not scramble the yolks in the next step.
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3
Add the egg yolks to the warm reduction in a heatproof bowl set over a pan of barely simmering water, ensuring the base of the bowl does not touch the water. Whisk continuously over this gentle heat. This is where the dish lives or dies: if the heat is too high the yolks will scramble and the sauce cannot be recovered; if too low the emulsion will not form. The yolks are ready when they are thick, pale, and fall from the whisk in a slow, reluctant ribbon.
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4
Remove the bowl from the heat. Begin adding the warm clarified butter in the thinnest possible stream, whisking constantly, incorporating each addition fully before adding more. As the emulsion tightens, the butter may be added in a slightly bolder stream. The sauce is stable when it is thick enough to coat the back of a spoon and does not run when a finger is drawn through it.
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5
Season with fine salt and a squeeze of lemon juice. Taste: the sauce should be rich, buttery, and bright at the edges. Fold in the finely chopped fresh mint leaves at the last moment. The mint should be detectable on the nose immediately — its volatile menthol oils announce themselves before the sauce reaches the palate. Do not return the sauce to heat after this point.