01 - Heat a large skillet over medium heat. Add the ground beef and cook, breaking it up with a spatula, until browned and no longer pink, approximately 5 minutes. Drain excess fat if necessary.
02 - Add the chopped onion, green bell pepper, and minced garlic to the skillet with the beef. Cook for 3-4 minutes until the vegetables are softened and fragrant.
03 - Pour in the tomato sauce, ketchup, tomato paste, Worcestershire sauce, brown sugar, mustard, smoked paprika, chili powder, salt, and black pepper. Stir thoroughly to incorporate all ingredients and create a uniform sauce.
04 - Reduce heat to low and let the mixture simmer uncovered for 10-12 minutes, stirring occasionally to prevent sticking, until the sauce has thickened to your desired consistency.
05 - While the filling simmers, butter the cut sides of the hamburger buns if desired. Toast them in a separate skillet or under the broiler until golden brown and lightly crisp.
06 - Spoon generous portions of the beef mixture onto the bottom halves of the toasted buns. Place the top halves on top and serve immediately while hot.