Preheat the oven to 425°F (220°C). Pat the Center-Cut Beef Tenderloin (Chateaubriand Roast) dry and season generously all over with Kosher Salt and freshly ground Black Pepper.
Heat a large ovenproof skillet over high heat until very hot, add a splash of Neutral Oil and a knob of Unsalted Butter. When the fat is shimmering, sear the roast on all sides until deeply browned, adding a few sprigs of Thyme and crushed cloves of Garlic to the pan for flavor as you turn it.
Transfer the skillet to the oven and roast the meat until it reaches your desired doneness (about 15–25 minutes for medium-rare, depending on size). Remove the roast to a cutting board, tent loosely with foil and let rest at least 10–15 minutes before slicing.
While the beef rests, make the Béarnaise: in a small saucepan combine White Wine Vinegar, Dry White Wine, finely minced Shallot, a few crushed Black Peppercorns and a couple of Tarragon stems; simmer until reduced to a few tablespoons. Strain the reduction into a heatproof bowl.
Place the bowl over a bain-marie (gentle simmer) and whisk in the Egg Yolks until the mixture is thickened and warm. Slowly drizzle in warm Clarified Butter, whisking constantly to create a smooth emulsion. Finish the sauce with a pinch of Salt, a little Lemon Juice to taste and chopped Tarragon and Chervil. Keep warm.
Prepare the potatoes: place the Waxy Potatoes in a pot with cold Water and a pinch of Salt, bring to a boil and cook until just tender. Drain, cool slightly and slice or halve.
In a skillet heat a little more Neutral Oil with a knob of Unsalted Butter and fry the potato pieces over medium-high heat until golden and crisp. Season with Salt and Black Pepper, then toss with chopped Flat-Leaf Parsley.
Toss the Watercress with a squeeze of Lemon Juice, a pinch of Salt and a drizzle of neutral oil if desired for a quick, peppery salad.
To serve: slice the rested roast, arrange on warm plates with the crisp potatoes and watercress, and spoon the warm Béarnaise over the beef or serve it on the side.
