01 - Set a large cast-iron skillet or 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 and press down firmly with a sturdy metal spatula to form thin patties with jagged, irregular edges. Season the top side with salt and pepper.
04 - Let the patties cook undisturbed for about 2 minutes until the edges turn deeply browned and crispy. Flip each patty and cook for another 1 to 2 minutes, then remove from the pan and set aside.
05 - Lower the heat to medium. Add the chopped onion, bell pepper, and a pinch of salt to the same skillet. Sauté until the vegetables soften, 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 to combine all the flavors.
07 - Pour in the beef broth and let the mixture simmer for 2 minutes so the flavors meld together.
08 - Return the smashed patties to the skillet and break them into chunks with your spatula, folding them 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 skillet with a lid or foil for about 30 seconds until the cheese melts into gooey perfection.
10 - While the cheese melts, spread butter on the cut sides of each bun and toast them in a separate skillet or on the griddle until golden brown.
11 - Spoon a generous portion of the cheesy beef mixture onto the bottom half of each toasted bun. Top with dill pickle chips, shredded lettuce, and tomato slices as desired. Cap with the top bun and serve immediately while hot.