For filet mignon that is supremely tender and stress-free, slow and steady wins the race. Skip the smoking-hot pan and the oven finish. Instead, flip often in a medium-hot skillet and baste with butter. The moderate temperature develops a browned crust without toughening the meat and makes hitting the ideal temperature for a rosy-pink center much easier. It's like a culinary version of the tortoise and the hare. The butter, studded with black pepper, adds a spicy richness to the lean and mild meat, though feel free to add smashed and peeled garlic and rosemary or thyme sprigs to the pan as well. Serve alongside a <a href="https://cooking.nytimes.com/recipes/1019392-wedge-salad"><span>wedge salad</span></a>, <a href="https://cooking.nytimes.com/recipes/3869-sauteed-spinach?smid=ck-recipe-iOS-share"><span>sautéed spinach</span></a> and <a href="https://cooking.nytimes.com/recipes/1020572-creamy-double-garlic-mashed-potatoes"><span>mashed potatoes</span></a>.
Season the steaks generously all over with salt. (You can season and refrigerate the steaks uncovered up to 24 hours ahead.)
Heat a large cast-iron skillet over medium. Add the oil and swirl to coat, then add the steaks and cook, flipping every minute, until crusty and browned, 6 to 8 minutes total.
Add the butter and black pepper. Tilt the pan and use a spoon to baste the steaks with the butter for 1 minute. Flip the steaks. Continue to baste and flip every minute until the steak registers an internal temperature of 120 to 125 degrees for medium-rare or 130 to 135 degrees for medium, 2 to 6 minutes more. Transfer meat to a plate, pour over the pan drippings and let rest for 5 minutes before serving.