Preheat oven to 350°F. Trim excess fat off ribs and brush both sides with vegetable oil. In a bowl, mix brown sugar, paprika, cumin, pepper and salt. Rub mixture evenly over ribs. Place ribs in a large roasting pan and pour in 1 cup water. Cover with aluminum foil and bake until tender, 1 1/2 hours.
In a small pan, mix rum, sugar, tomato paste, Worcestershire sauce and Tabasco. Bring to a boil over medium heat; cook for 5 minutes, stirring occasionally. Remove foil from roasting pan, pour off all but 1/2 cup of liquid in pan and pour rum mixture over ribs. Return pan to oven and continue baking, uncovered, turning ribs several times and basting with liquid in pan, until meat starts to pull away from bones and is very tender, about 1 hour. Add a little water as necessary to prevent scorching.
Let ribs rest on a cutting board for 5 minutes. Slice into individual portions and serve hot with barbecue sauce on the side, if desired.