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 needed.
02 - Add the chopped onion, green bell pepper, and minced garlic to the skillet. Cook for 3 to 4 minutes, stirring occasionally, until vegetables are softened and fragrant.
03 - Pour in the tomato sauce, ketchup, tomato paste, and Worcestershire sauce. Add the brown sugar, yellow mustard, smoked paprika, chili powder, salt, and black pepper. Stir thoroughly to combine all ingredients.
04 - Reduce heat to low and let the mixture simmer uncovered for 10 to 12 minutes, stirring occasionally. Allow the sauce to reduce and thicken to your desired consistency.
05 - While the filling simmers, optionally butter the cut sides of the hamburger buns. Toast them in a skillet or under the broiler until golden brown and lightly crisped.
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.