In Dutch oven or large skillet (preferably iron) brown flour in oil until it is deep red-brown, stirring constantly to prevent burning. Add onions, celery, green pepper, and garlic. Cook until vegetables are tender. Stir in beef, pork, giblets, and seasonings. Continue cooking until meat loses its color. Blend in broth; cover and simmer 25 minutes. Stir in rice and onion tops. Cook 5 minutes longer. Mixture should be slightly moist.