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1
The evening before service, set the trimmed, tied fillet on a rack and leave it uncovered in the refrigerator overnight. The surface must be visibly dry and slightly tacite to the touch before it meets the pan — this is the condition for superior Maillard development.
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2
One hour before cooking, remove the fillet from the refrigerator and season all surfaces with fine sea salt and black pepper. Allow it to approach room temperature.
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3
For the Béarnaise, combine the vinegar, white wine, shallots, tarragon stems, and crushed peppercorns in a small saucepan. Reduce over medium heat until approximately 20 ml of liquid remains. Pass through a fine sieve and allow to cool. The reduction must be pungent with tarragon and sharp with acid.
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4
Whisk the egg yolks with the cooled reduction in a bain-marie set over barely simmering water, working continuously until the mixture ribbons and the whisk leaves a clear trail on the base of the bowl. Remove from the heat and incorporate the warm clarified butter in a thin, steady stream, whisking without pause. Fold in the chopped tarragon leaves and correct the seasoning. The finished sauce coats the back of a spoon and does not flow when the spoon is drawn across — this is where the Béarnaise lives or dies.
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5
For the Pommes Château, melt the butter in a heavy ovenproof sauté pan over medium heat. Add the turned potatoes and colour them on all sides until a light golden crust forms. Transfer to the 200°C oven alongside the fillet (step 7) and roast, turning once, until a skewer enters without resistance — approximately 25–30 minutes.
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6
Place a heavy cast-iron or carbon-steel pan over the highest available heat until it begins to smoke. Add the clarified butter. Season the fillet once more lightly. Lay it in the pan and sear for 2 minutes per side on all surfaces — including both flat ends — pressing gently with tongs to ensure full contact. The crust must be dark mahogany and unbroken across every surface.
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7
Transfer the seared fillet, still in its pan or moved to a small roasting tray, to a 200°C oven. Roast for 12–15 minutes, turning once at the midpoint. Begin probing at 12 minutes: remove the fillet when the centre registers 50–52°C for rare (the classical service) or 54–56°C for medium-rare. The fillet is lean; cooking beyond this point produces irreversible dryness.
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8
Transfer the fillet to a warm rack set over a tray. Rest, uncovered, for a minimum of 10 minutes. Carryover will raise the internal temperature by 5–6°C. At the end of the rest, the exterior should feel firm at its crust and yielding beneath — the juices, when the string is cut and a finger pressed at the centre, must not run freely.
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9
Remove the string. Carve at the table into slices of 1.5 cm against the grain. The interior must be uniformly rose from the outermost edge to the centre — no grey band. Serve immediately with the Sauce Béarnaise and Pommes Château.