1In a large skillet, cook the ground beef over medium heat until browned. Drain any excess fat.
Add the chopped onion and green bell pepper to the skillet. Cook until the vegetables are tender, about 5 minutes.
Stir in the BBQ sauce, ketchup, Worcestershire sauce, brown sugar, and smoked paprika. Mix well to combine.
Reduce the heat to low and let the mixture simmer for about 10 minutes, stirring occasionally.
Toast the hamburger buns if desired.
Spoon the BBQ sloppy joe mixture onto the bottom halves of the hamburger buns.
Place the top halves of the buns on top and serve immediately.