• Preheat the oven to 400°F. Season the beef liberally on all sides with salt and pepper and set it aside to come to room temperature while you make the Béarnaise sauce.

Make the Béarnaise sauce

• Combine the vinegar, wine, shallots, tarragon leaves, peppercorns, and salt in a small saucepan over medium-high heat. Bring to a rapid simmer and cook for 6 to 8 minutes, or until reduced by about 75%.
• Set aside to cool for a few minutes, then strain into a small bowl, pressing the shallot mixture with the back of a spoon to squeeze out all of the liquid. You should have about 2 tablespoons. If you're short, just add a little water to make up the difference.
• Rinse and dry the saucepan and add the butter. Melt completely over medium heat and set aside for 2 to 3 minutes. Carefully skim off most of the foam that forms with a spoon and set aside. Removing the foam helps the sauce to emulsify.
• Place 1/2 to 3/4-inch of water in a saucepan and bring to a simmer over medium heat. Find a heatproof bowl that will fit over the simmering water without actually touching it during cooking. A distance of about 1-1/2 inches between the water and the bottom of the bowl is ideal. We generally use a stainless mixing bowl over a 2-quart saucier.
• Place the egg yolks and strained vinegar mixture into the heatproof bowl and whisk together until blended. Set the bowl over the simmering water and whisk vigorously. As the eggs thicken and increase in volume, scrape the sides frequently to keep the mixture cooking evenly. You must whisk continually until the eggs have thickened to the point where you can see thin ribbons form when you lift the whisk. This should take about 5 minutes.
• To finish the sauce, whisk in the melted butter in a very slow drizzle. The sauce will thicken and develop a glossy sheen.
• To keep the Béarnaise warm for just a few minutes while you cook the beef, you can simply remove the pan from the stove and leave it in the bowl above the hot water. For longer storage, transfer it to a large insulated mug or thermos.

Roast the beef

• Heat the olive oil in a heavy, ovenproof skillet over medium-high heat. Add the beef and sear until lightly browned on all sides, turning with tongs as needed, about 3 minutes total.
• Place the skillet in the oven and roast for 10 to 12 minutes, until an instant-read thermometer registers 125° for medium rare. Tent with foil and allow to rest for 20 minutes before carving.