Béarnaise

Combine the vinegar, minced shallot, tarragon stems (reserve the leaves), and cracked peppercorns in a small saucepan. Simmer gently until the liquid reduces to about two tablespoons of intensely flavored, syrupy essence. Strain out and press the solids, discarding the stems, shallot, and pepper — you want only the perfumed, acidic liquid. Let it cool to warm before it meets the yolks; hot reduction would start to cook them.

Set a heatproof bowl over a pan of barely simmering water — the bowl must not touch the water, and the water must steam, not boil. Add the yolks and the cooled tarragon reduction. Whisk constantly and vigorously, lifting the bowl off the heat every few seconds to control the temperature, until the yolks triple in volume and thicken to a pale sabayon that holds a ribbon. Too much heat scrambles the yolks; too little and they never thicken enough to carry the butter.

Off the heat (or with the bowl resting on a damp towel for stability), begin adding the warm clarified butter in a thin, steady stream while whisking without pause. Start drop by drop until the emulsion takes and visibly thickens, then increase to a slow trickle. Keep the butter warm, not hot — around 40-50 C / 105-120 F — and the sabayon warm too, so droplets disperse evenly. Add butter faster than the yolks can absorb it, or let either component get cold, and the emulsion breaks.

Whisk in a generous spoonful of the reserved fresh tarragon leaves, finely chopped, then season with salt and a small pinch of cayenne. Taste: the reduction already supplies the acidity, so the fresh tarragon is for green, anise-bright lift and flecks of color. Adjust salt only — do not add lemon. The sauce should taste rich, tangy, and unmistakably of tarragon.