In a large skillet over medium-high heat, cook the diced onion and green pepper for 4 minutes until softened.
Add the garlic and cook 30 seconds. Add the ground beef and cook until browned, about 7 minutes. Drain excess fat.
Stir in the tomato sauce, ketchup, brown sugar, mustard, Worcestershire sauce, vinegar, salt, and pepper.
Reduce heat to medium-low and simmer uncovered for 10–15 minutes, stirring occasionally, until thick and saucy.
Toast the hamburger buns lightly under the broiler or in a toaster.
Spoon the meat mixture generously onto the bottom buns, top with the other half, and serve immediately.
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