Make the béarnaise reduction first: combine 1/4 cup White Wine Vinegar, 1/4 cup Dry White Wine, 1 small minced Shallot, a teaspoon of crushed Peppercorn and a few sprigs/stems of Tarragon in a small saucepan; simmer until reduced to about 2–3 tablespoons, then cool and strain into a bowl, discarding solids.
Prepare the fries: peel (optional) and cut 1.5–2 lb of Starchy Potatoes into 1/3–1/2" batons, then rinse and soak them in cold Water for 20–30 minutes to remove excess starch; drain and dry very thoroughly on clean towels.
Par-cook the fries: heat a deep pot or fryer with enough Neutral Frying Oil to submerge the potatoes to about 160°C / 325°F. Fry the dried potatoes in batches until just tender but not colored, 4–6 minutes. Remove to a wire rack or paper towel-lined tray and let cool.
Finish the béarnaise: set a heatproof bowl over gently simmering water (bain-marie). Whisk 3 Egg Yolks with 1–2 tablespoons of the strained reduction until thick and pale. Slowly drizzle in 10–12 tablespoons of warm Clarified Butter, whisking constantly until the sauce is glossy and emulsified. Stir in finely chopped leaves of the reserved Tarragon and 1 tablespoon of chopped Chervil, then season to taste with Salt and freshly ground Black Pepper. Keep warm (off direct heat) until serving.
Season and sear the steak: pat the Ribeye Steak dry and season both sides generously with Salt and Black Pepper. Heat a heavy skillet over high heat until very hot, add a knob of Butter and a splash of the Neutral Frying Oil to prevent burning. Sear the steak 2–3 minutes per side for medium-rare (adjust time to thickness), adding crushed cloves of Garlic and sprigs of Thyme to the pan and continuously spooning the melted butter and aromatics over the steak to baste.
Rest the steak: transfer the seared steak to a cutting board and let rest for 5–10 minutes so the juices redistribute.
Crisp the fries: raise the oil temperature to 190–200°C / 375–400°F and return the cooled fries in batches, frying until golden brown and extra-crispy, 2–4 minutes. Drain on paper towels and immediately season with a pinch of Salt.
To serve: slice the rested Ribeye Steak against the grain, arrange alongside the hot frites, and spoon the warm béarnaise over the steak or serve it on the side for dipping. Garnish with an extra sprinkle of chopped Tarragon or Chervil if you like.
