Butterfly leg of lamb or have your butcher do it for you. In a nonreactive bowl or pan, cover meat with yogurt, turning to coat evenly. Marinate, covered and refrigerated, for at least 12 hours or overnight. Remove from marinade and pat dry with paper towels.
On a cutting board cover garlic with salt. Mince and flatten with side of a heavy knife until garlic forms a paste. Scrape into a small bowl and mix well with remaining spices. Rub butterflied leg of lamb with spice mixture. Cover tightly and marinate, refrigerated, at least 8 hours or overnight.
Heat a grill or broiler until very hot. Cook on grill or broiler rack, 10 to 15 minutes each side, for rare to medium-rare meat. Remove lamb to a carving board, cover loosely with foil and let sit 10 minutes before carving into thin slices.