Contrary to American versions of the dish, Turkish shish kebab rarely comes with vegetables on the same skewer as the meat. Rather, the vegetables are grilled on separate skewers, so each can be cooked the proper length of time.
Step 1: Combine the yogurt, olive oil, garlic, pepper flakes, salt, and black pepper in a nonreactive bowl. Add the lamb cubes and toss to coat thoroughly. Let the lamb marinate in the refrigerator, covered, for 24 hours, stirring once or twice.
Step 2: Remove the lamb from the marinade and discard the marinade. Thread the cubes of meat onto the thin skewers, alternating lean and fatty pieces. Thread the tomatoes onto a separate, flat skewer; thread the bull’s horn peppers onto another flat skewer.
Step 3: Set up the grill for direct grilling and preheat to high.
Step 4: When ready to cook, brush and oil the grill grate, then arrange all of the kebabs on the hot grate, and grill, turning with tongs, until the skins on the vegetables are blistered and browned and the lamb is browned and done to taste, 8 to 12 minutes in all for well-done.
Step 5: Using a pita to protect your hand, unskewer the lamb and vegetables onto serving plates, dividing the vegetables evenly. Serve at once, accompanied by the pitas and sumac (if using) for sprinkling on top.