In a large skillet over medium high heat brown ground beef, celery, green pepper, mushrooms, and onion. Drain any excess fat. Stir in tomato sauce, ketchup, barbeque sauce, brown sugar, dry mustard, salt and pepper, Worcestershire sauce, and vinegar.
Cover and simmer for 15-20 minutes stirring occasionally. If after 20 minutes the mixture still seems too watery, simmer for a little longer until the mixture has thickened.
Serve on a bun and top with a slice of provolone cheese.