Before you start, decide if you want your lamb chops rare or medium. If you want your lamb chops rare in the center, you can cook them entirely on the stovetop.
If you want them a bit more cooked, and you have double rib chops (2 ribs per piece of meat, each piece of meat about 1/4 of a pound), you will want to finish them in the oven, at 400°F for a few minutes.
Or you can cover the pan and remove from the heat and just let sit for a few minutes.
1 Marinate the lamb chops with rosemary, salt, pepper, garlic, olive oil: In a small bowl, mix the rosemary, salt, pepper, garlic, and 2 tablespoons of the olive oil together. Coat the lamb chops with the mixture, massaging it into the meat with your fingers. If you are working with double rib chops, cover and let stand at room temperature for 30 to 45 minutes.
If you are working with single rib chops, and you want the result to be rare, let the chops sit in the rub in the refrigerator, do not let come to room temp or the thin ribs will easily overcook when you sear them in the next step.
2 Sear the lamb chops: Heat the remaining 2 tablespoons olive oil in an oven-proof sauté pan over high heat. When the oil is shimmering hot, sear the lamb chops on all sides, about 2 to 3 minutes per side.
(If you are working with single rib chops, sear only on two sides, and only a minute or so on each side if you want the result to be rare or medium rare.)
3 Test for doneness, if you want more well done, finish in oven, otherwise tent with foil and let rest: At this point, if you want your lamb chops rare, they are likely cooked enough. Remove them from the pan, cover them with foil and let sit for 5 to 10 minutes before serving.
If you would like your chops more cooked, you can put them in a 400°F oven for 3 to 5 minutes, or keep them in the hot pan, remove from heat, and cover the pan for a few minutes.
Then remove from the pan to a plate or cutting board, cover with foil and let rest 5 to 10 minutes before serving.