The ribs are simmered until tender then coated in barbecue sauce to make a hearty topper for the flavorful soup.
In a 4-quart Dutch oven, heat oil over medium-high heat. Add short ribs, half at a time if necessary; cook until browned on all sides, turning to brown evenly. Remove meat and set aside. Add onion, celery, carrots, undrained chile peppers and chili powder. Cook, uncovered, over medium heat for 5 minutes, stirring frequently. Return short ribs to Dutch oven.
Add beans and broth. Bring to boiling; reduce heat. Simmer, covered, about 2 hours or until ribs are tender, stirring occasionally. Remove ribs from Dutch oven. Stir in undrained tomatoes. Heat through. Keep warm while meat finishes cooking.
Line a shallow roasting pan with a double thickness of foil. Place ribs in pan. Brush with half of the barbecue sauce. Bake in a 350 degree F oven for 10 minutes. Turn ribs; brush with remaining barbecue sauce. Bake about 10 minutes more or until edges of ribs are crisp.
Season soup with salt and pepper to taste. To serve, divide ribs among 8 shallow soup dishes and ladle soup over ribs. If you like, garnish with celery leaves. Makes 8 main-dish servings (10 cups soup plus meat).