01 - Set a large cast-iron skillet or flat griddle over medium-high heat and allow it to get ripping hot, about 3 to 4 minutes.
02 - Gently divide the ground beef into 4 loosely packed balls, handling the meat as little as possible to keep it tender.
03 - Place the beef balls onto the hot skillet. Press down firmly with a sturdy metal spatula to flatten into thin patties with jagged, irregular edges. Season the top side with salt and pepper.
04 - Let the patties cook without moving for about 2 minutes until the edges turn deeply browned and crisp. Flip and cook another 1 to 2 minutes. Transfer to a plate and set aside.
05 - Lower the heat to medium. Add the chopped onion and diced bell pepper to the same skillet with a pinch of salt. Sauté until softened and translucent, about 3 to 4 minutes. Stir in the minced garlic and cook for 30 seconds until fragrant.
06 - Stir in the ketchup, tomato paste, yellow mustard, smoked paprika, Worcestershire sauce, and chili powder if using. Mix thoroughly and let the mixture cook for about 1 minute to toast the spices.
07 - Pour in the beef broth and bring to a gentle simmer. Let it reduce for about 2 minutes so the flavors concentrate and meld together.
08 - Return the smashed patties to the skillet. Break them apart with your spatula into bite-size crumbles and fold everything together. Continue cooking for 2 to 3 minutes until the sauce thickens and clings to the beef.
09 - Lay 1 slice of cheese over each mound of saucy beef. Cover the skillet with a lid or foil and let it steam for about 30 seconds until the cheese is fully melted and gooey.
10 - While the cheese melts, spread butter on the cut sides of each bun. Toast in a separate skillet or on the griddle over medium heat until golden brown and lightly crisped.
11 - Spoon a generous portion of the cheesy beef mixture onto the bottom half of each toasted bun. Layer with pickle chips, shredded lettuce, and tomato slices to taste. Cap with the top bun and serve immediately while hot.