Season lamb loin chops with salt and pepper on both sides. Place lamb in the cast iron skillet with the fat side down. Cook for 3-4 minutes on each side.
Remove the lamb from the pan and place on a sheet tray with a rack, place in the oven for 5 – 7 minutes. Once removed from the oven, allow the lamb loin chops to rest for 2-3 minutes so juices can settle, drizzle the sherry vinegar, and tomato butter sauce over the lamb chops.
