01 - Place a large cast-iron skillet or griddle over medium-high heat and allow it to get thoroughly hot.
02 - Divide the ground beef into 4 loosely packed balls, handling the meat as little as possible to keep it tender.
03 - Once the skillet is ripping hot, set the beef balls in the pan. Press down firmly with a sturdy metal spatula to flatten into thin patties with jagged, lacy edges. Season the top side with salt and pepper.
04 - Let the patties cook without moving them for about 2 minutes until the edges turn deeply browned and crisp. Flip and cook for another 1 to 2 minutes on the second side. Remove the patties and set aside on a plate.
05 - Lower the heat to medium. Add the chopped onion, diced bell pepper, and a pinch of salt to the same skillet. Sauté until the vegetables have softened, about 3 to 4 minutes. Stir in the minced garlic and cook for 30 seconds longer until fragrant.
06 - Stir in the ketchup, tomato paste, yellow mustard, smoked paprika, Worcestershire sauce, and chili powder if using. Mix everything thoroughly to combine.
07 - Pour in the beef broth and let the mixture simmer for 2 minutes so the flavors come together.
08 - Return the smashed beef patties to the skillet. Break them up with your spatula and fold the pieces into the sauce. Continue cooking for 2 to 3 minutes until the mixture thickens slightly.
09 - Lay 1 slice of cheese over each mound of the beef mixture. Cover the pan with a lid for about 30 seconds to let the cheese melt evenly.
10 - While the cheese melts, spread butter on the cut sides of each bun. Toast them in a separate skillet or on the griddle over medium heat until golden brown.
11 - Spoon the cheesy beef mixture generously onto the bottom half of each toasted bun. Add pickle chips, shredded lettuce, and tomato slices as desired. Cap with the top bun and serve immediately while hot.