Heat the olive oil in a large skillet over medium heat. Add the ground beef and cook until browned, breaking it apart with a wooden spoon. Drain excess grease if needed.
Add the diced onion, bell pepper, and garlic to the skillet. Cook for 3–4 minutes, stirring often, until the vegetables soften and the kitchen smells fragrant.
Stir in the ketchup, tomato paste, brown sugar, mustard, Worcestershire sauce, chili powder, paprika, salt, and pepper. Mix well until the beef is coated in the sauce.
Add the water or broth to loosen the mixture slightly. Let the sloppy joe filling simmer on low heat for 10–15 minutes, stirring occasionally, until the sauce thickens and clings to the meat.
Taste and adjust seasoning as needed. If you like it sweeter, add a pinch more sugar. For tangier flavor, add an extra squeeze of mustard.
Spoon the saucy meat mixture onto toasted hamburger buns. Serve with pickles, cheese slices, or a scoop of coleslaw if desired.
Enjoy warm with plenty of napkins.