Chateaubriand with Bearnaise Sauce

To make the herb rub, in a small bowl, mix together the thyme, paprika, garlic powder, lemon pepper, and salt. Rub the beef with 1 Tbsp of the olive oil. Sprinkle the herb rub all over the beef. Let stand at room temperature for at least 15 min or up to 1 hour before cooking. Preheat overn 400 degrees Coat the bottom of a large, heavy, ovenproof frying pan with the remaining 1 Tbsp oil and heat over high heat. Add the steak and sear on both sides until nicely browned, 3-5 min total. Transfer the pan to the oven and roast to the desired doneness, 10-20 min longer. Test for doneness using an instatn-read thermometer or by cutting into the meat. Remove the steak from the oven when it is red at the center for rare (120 degrees F) or deep pink at the center for medium-rare (130 degrees F). Transfer to a carving board and let rest, tented loosely with aluminum foil, while you make the sauce. To make the sauce, combine the wine, vinegar, shallot, tarragon, and 1/2 tsp pepper in a small saucepan and bring to a boil. Cook until reduced by two-thirds, 3-5 min. Transfer to a heatproof bowl, stir in the lemon juice, and let cool. Place the bowl with the reduced wine mixture over a saucepan of simmering water (but not touching the water). Whisk the egg youlks into the wine mixture. Heat gently over the hot water, whisking constantly, until the mixture begins to thicken, 2-3 min. Remove from the heat and whisk in the butter to form a thick sauce. If it seems too thin, replace the bowl over the hot water and heat briefly, whisking constantly, until thickened. Season to taste with salt and pepper. Slice the steak thickly on the diagonal across the grain and pass the sauce in a gravy boat.