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Let beef stand at room temperature for 1 hour before roasting. Set an oven rack in the middle position and preheat the oven to 400°F.
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Season the beef all over with kosher salt and pepper. Heat the oil in an oven-proof skillet over medium-high heat until almost smoking. Cook, turning with tongs, until well browned on all but one side, about 10 minutes total. Turn the tenderloin so that the un-seared side is down, and transfer the skillet directly to the preheated oven. (If your pan isn't oven-proof, transfer the beef to a lightly oiled roasting pan.) Roast until an instant-read thermometer inserted into the center of the meat registers 120°F-125° for medium rare, about 15 minutes, or until done to your liking (115°F-120°F for rare, 130°F-135°F for medium). Keep in mind that these temperatures account for the fact that the temperature will continue to rise about 5 degrees while the meat rests.
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Transfer the roast to a carving board (preferably with a well for collecting juiceand let it rest, covered loosely with aluminum foil, for 10 to 15 minutes. Place a dishtowel or oven mitt over the handle of the roasting pan to remind yourself that it's hot.
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Meanwhile, carefully discard the fat from the roasting pan (remember that the handle is hot!). Set the pan on the stovetop and add the beef broth. Bring the broth to a boil, using a wooden spoon to scrape the fond, or brown bits, from the bottom of the pan. Add the flavorful broth to the red wine sauce, and then bring the sauce to a simmer.
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Carve the tenderloin into 1/3-inch-thick slices. Serve the beef, passing the red wine sauce at the table.