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Step 1
Let steak sit at room temperature 30 minutes before cooking, which will help it cook quickly and more evenly.
Step 2
Heat broiler. Heat a large skillet, preferably cast iron, over medium-high heat, then heat oil in pan until smoking. Season steak very generously with salt and pepper and cook until a deep brown crust forms on underside (do not turn), about 4 minutes. Transfer steak to a cutting board, turning it browned side up.
Step 3
Cut meat from bone in 2 pieces (strip steak and filet mignon). Slice both pieces straight down perpendicular to the bone 1” thick. Replace sliced steak around the bone (it should look like a whole sliced steak) and return to skillet, browned side up. Top with butter and broil until butter is melted and steak is medium-rare, 4–6 minutes. Serve steak with buttery pan juices spooned over.