Cut the lamb into strips about 1/2 inch (1.3 cm) wide and 2 inches (5 cm) long. Keep the fat and try to leave some lean attached to it.
Crush the garlic enough to loosen the peel, then peel it and discard the peel.
Toss lamb with olive oil, salt, pepper, marjoram, and garlic until coated. Marinate 2 hours at room temperature, or 4 to 6 hours in the refrigerator, turning occasionally. If refrigerated, let it stand out at least 30 minutes before cooking.
Preheat the broiler or prepare very hot coals (or hot embers).
Turn the lamb once more, then skewer the strips, piercing each piece in at least two places.
Cook as close as possible to the heat source. Cook 3 minutes on one side, then 2 to 3 minutes on the other, until a fine crust forms. Serve immediately.