Brown beef in a large skillet over medium-high heat for 8 to 10 minutes, breaking it into small crumbles, until it reaches 160°F. Drain excess fat.
Transfer beef to a 4- to 6-quart slow cooker. Stir in onion, pepper, tomato sauce, ketchup, tomato paste, molasses, vinegar, Worcestershire, mustard, broth, salt and pepper.
Cover and cook on low for 6 hours, stirring once if convenient, until the vegetables are soft and the filling is thoroughly hot.
If the sauce is loose, uncover and cook on high for 15 to 20 minutes, stirring, until it clings to the beef. Keep hot at 140°F or above if holding for serving.
Toast the split buns and divide the filling among them as people are ready to eat.