Preheat oven to 325 degrees.
Heat oil over medium heat in a large, heavy, oven-safe pot or Dutch oven, and brown the ribs on all sides, about 5 minutes, working in batches if necessary. Sprinkle ribs with salt and black pepper as they brown. Transfer cooked ribs to paper towels to blot up extra oil.
Stir the onion rings and carrots into the same pot, and cook and stir until the onions turn translucent and start to brown, about 8 minutes. Stir in the garlic, and cook until fragrant, about 1 more minute. Mix in tomato sauce, barbecue sauce, and beef broth; bring the sauce to a boil, and simmer for 1 minute to blend flavors. Stir in the browned ribs.
Cover the pot, and bake in the preheated oven until the rib meat is very tender, about 2-1/2 hours. Turn the ribs occasionally while cooking. Season to taste with salt and black pepper before serving hot.