In a large skillet over medium heat, cook the ground beef until browned. Drain any excess fat.
Add the chopped onion and green bell pepper to the skillet. Cook for 5 minutes or until softened.
Stir in ketchup, tomato paste, Worcestershire sauce, brown sugar, garlic powder, and smoked paprika. Mix well.
Reduce the heat to low and let the mixture simmer for 10 minutes. Stir occasionally to prevent sticking.
Toast the hamburger buns if desired. Spoon the sloppy joe mixture onto the buns and serve hot.