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For the steaks: Pat steaks dry with paper towels, coat with olive oil, and set aside to come to room temperature, at least 5 minutes.
Heat a large seasoned cast iron skillet or large frying pan over medium-high heat until hot but not smoking, about 3 minutes. Place steaks in pan and cook, undisturbed so they can get well-browned, about 5 minutes per side for medium-rare. Remove steaks to a dish, top with pats of compound butter, and let rest 10 minutes before serving.