In a nonstick 12-inch skillet, heat oil over medium heat. Add onion and garlic and cook until onion is tender, about 5 minutes.
Add red and green peppers and celery and cook until tender, about 5 minutes. Stir in ground beef and cook, breaking up meat with side of spoon, until meat is no longer pink, about 5 minutes. Stir in tomatoes with their puree, molasses, vinegar, slat, and black pepper and heat to boiling. Reduce heat and simmer until sauce has slightly thickened, about 10 minutes.
Place split buns on plates and top with Sloppy Joe mixture.
Recipe courtesy The All New Good Housekeeping Cookbook