In a large cast iron skillet over medium heat, cook the ground beef until completely browned, about 7 minutes. Add the chopped onion and bell pepper. Season with salt and pepper, to taste. Cook until the vegetables are tender, about 7 additional minutes.
Stir in the ketchup, vinegar, Worcestershire sauce, brown sugar, mustard and barbecue sauce. Lower the heat to simmer the mixture until it thickens, about 10 minutes. Stir in the Parmesan cheese.
Evenly pile the beef mixture on the toasted hamburger buns.
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