01 - Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it apart with a spoon, until browned and nearly cooked through, about 4 to 5 minutes. Drain excess fat if necessary.
02 - Add the chopped onion, green bell pepper, and minced garlic to the beef. Cook, stirring occasionally, until the vegetables are tender, approximately 3 to 4 minutes.
03 - Stir in the tomato sauce, tomato paste, ketchup, Worcestershire sauce, brown sugar, yellow mustard, smoked paprika, chili powder, salt, and black pepper. Mix thoroughly to blend the flavors.
04 - Reduce heat to low and let the mixture simmer uncovered for 8 to 10 minutes, stirring occasionally until thickened to desired consistency.
05 - Spoon the hot beef mixture onto the bottom halves of the toasted hamburger buns. Add sliced pickles or shredded cheddar cheese if preferred, then cover with the top bun. Serve immediately.