Prepare the Vegetables. Chop the onion and green bell pepper, and mince the garlic. Set aside.
Cook the Ground Beef. In a large skillet over medium-high heat, cook the ground beef until browned and fully cooked, breaking it up with a spatula as it cooks. Drain any excess fat.
Add the Vegetables. Add the chopped onion, bell pepper, and minced garlic to the skillet with the ground beef. Cook for about 5 minutes, or until the vegetables are softened.
Combine Sauce Ingredients. Stir in the ketchup, brown sugar, Worcestershire sauce, yellow mustard, tomato paste, and smoked paprika. Mix well to combine.
Simmer. Reduce the heat to medium-low and let the mixture simmer for about 10-15 minutes, stirring occasionally, until the sauce thickens and the flavors meld together. Season with salt and pepper to taste.
Serve. Spoon the sloppy joe mixture onto hamburger buns. Serve hot with your favorite side dishes.