Heat oil in a medium saucepan over medium heat. Add onion and pepper and sauté for 5 – 7 minutes or until onions are translucent. Add garlic and brown sugar and cook for 2 minutes more. Stir in remaining ingredients and simmer for 30 minutes over low heat.
Rub duck halves with olive oil, salt and pepper. Grill over white-hot coals until medium-rare. Just before serving, baste with barbecue sauce.