Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it into small crumbles, until browned and it reaches 160°F (71°C). Drain excess fat if needed.
Add the onion and bell pepper. Cook for 4 to 5 minutes until softened, then stir in the garlic for 30 seconds.
Stir in the ketchup, tomato paste, broth, Worcestershire sauce, brown sugar, mustard, salt, and pepper until combined.
Reduce the heat and simmer uncovered for 10 to 15 minutes, stirring occasionally, until thick and saucy. Toast the buns if desired, spoon the filling onto them, and serve hot.