Heat a large skillet over medium heat. Add the ground beef and cook until browned, breaking it into crumbles with a wooden spoon. Drain any excess fat if needed.
Add the chopped onion, green bell pepper, and minced garlic to the skillet. Cook for 3–4 minutes until the vegetables are softened and fragrant.
Stir in the tomato paste, ketchup, brown sugar, Worcestershire sauce, mustard, salt, and pepper. Mix well to coat the beef mixture evenly.
Reduce the heat to low and let the mixture simmer for 10–12 minutes, stirring occasionally, until the sauce thickens and flavors meld.
While the filling simmers, toast the burger buns lightly on a skillet or in the oven.
Spoon a generous portion of the Sloppy Joe filling onto the bottom half of each bun. Add optional toppings like shredded cheese or pickles.
Place the top bun on and serve immediately with your favorite sides, such as fries or a fresh salad.