In a large saucepan, saute the onion, green pepper, oregano and cumin in oil until vegetables are tender. Add garlic; cook 1 minute longer.
Stir in the beans, pumpkin, tomatoes, broth, water, brown sugar, chili powder and pepper; bring to a boil. Reduce heat; cover and simmer for 1 hour. Add turkey; heat through. If desired, top with cheddar cheese.
