For the barbecue sauce: Place the tomato sauce, sugar, vinegar, tomato paste, balsamic vinegar, Worcestershire sauce, salt, cinnamon stick, garlic and onions in a medium saucepan. Bring the mixture to a simmer and cook, stirring occasionally, until thick, about 1 hour. Cool for 30 minutes. Remove the onion, garlic and cinnamon stick and discard. Refrigerate until ready to use (for up to 1 week).
For the lamb chops: Place a grill pan over medium-high heat or preheat a gas or charcoal grill. Spray the grill with vegetable oil cooking spray. Sprinkle the chops on both sides with the salt and pepper. Drizzle with the oil and sprinkle the herbes de Provence on both sides. Grill for 2 to 3 minutes on each side until medium-rare. Cool for 5 minutes and serve with the barbecue sauce.