In a glass baking dish just large enough to hold lamb chops in a single layer, combine olive oil, garlic, rosemary, mint, lemon juice, salt and pepper. Place lamb in the dish and turn to coat the chops with the marinade. Cover and refrigerate while you make the cucumber mint salsa. (If you marinate the lamb the night before, that’s even better!)

Preheat the oven to 250º F.

In a large skillet, heat oil over high heat until hot but not smoking. Remove chops from the marinade. Sear in 2 batches on both sides just to brown, then reduce the heat to medium-high and cook for about 4 minutes per side for shoulder chops, 2 1/2 minutes per side for rib chops, and 1 1/2 minutes per side for loin chops for medium-rare. Add another 20 to 30 seconds per side for medium-well done.

Put the first batch of chops on an ovenproof platter and place in the oven to keep warm while you cook the remaining chops.

Remove chops from the oven and let rest for 3 minutes to allow the juices to be reabsorbed. Spoon Cucumber Mint Salsa over the chops and serve immediately.