Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it apart as it cooks. If needed, drain off any excess grease.
When the beef is partly cooked but still a little pink, add the chopped onion and green bell pepper. Cook and stir until the beef is fully cooked and the vegetables are softened.
Add the minced garlic and cook for about 30 seconds, stirring gently so it does not burn. Lower the heat to medium-low.
Stir in the tomato sauce, ketchup, brown sugar, Worcestershire sauce, mustard, salt, and pepper. Mix everything until well combined.
Let the mixture simmer gently for about 10 minutes, stirring now and then, until it thickens to your liking.
Spoon the warm sloppy joe mixture onto toasted hamburger buns and serve right away.