1. Heat the olive oil in a large skillet over medium heat. Add the chopped onion and green bell pepper and cook for 4 to 5 minutes until softened. Stir in the garlic and cook for 30 seconds.

2. Add the ground beef and break it up with a spoon. Cook for 6 to 8 minutes until browned and no longer pink. Drain excess grease if needed.

3. Stir in the ketchup, tomato sauce, tomato paste, yellow mustard, Worcestershire sauce, brown sugar, apple cider vinegar, smoked paprika, salt, and black pepper until fully combined.

4. Reduce the heat to low and simmer the mixture for 10 to 15 minutes, stirring occasionally, until the sauce is thick and glossy.

5. Butter the buns lightly if desired and toast them in a skillet or under the broiler until golden.

6. Spoon the sloppy joe mixture onto the buns and serve warm.