Heat a large skillet over medium-high heat. Add the ground beef and cook until browned, breaking it up as it cooks. Drain excess grease, then add chopped onion, bell pepper, and garlic. Sauté for 3-4 minutes until softened.
Reduce the heat to medium and stir in tomato sauce, ketchup, Worcestershire sauce, brown sugar, mustard, smoked paprika, salt, and black pepper. Mix well and let the mixture simmer for 10-12 minutes, allowing the flavors to meld and the sauce to thicken.
While the meat mixture is simmering, heat a separate pan over medium heat. Spread butter on the inside of the buns and toast them until golden brown.
Spoon the saucy meat mixture onto the toasted buns. Serve hot with your favorite sides, like fries or coleslaw. Enjoy your homemade Sloppy Joes!