01 - Set a large cast-iron skillet or flat griddle over medium-high heat and allow it to get ripping hot, about 3 minutes.
02 - Gently divide the ground beef into 4 loose, evenly sized balls. Avoid pressing or overworking the meat to keep it tender.
03 - Place the beef balls onto the hot skillet. Using a sturdy metal spatula, press each ball firmly into a thin patty with jagged, irregular edges. Season the tops generously with salt and pepper.
04 - Let the patties cook without moving them for about 2 minutes until the edges are deeply browned and crisp. Flip each patty and cook 1 to 2 minutes more. Transfer to a plate and set aside.
05 - Reduce the heat to medium. Add the chopped onion and diced bell pepper to the same skillet with a pinch of salt. Sauté, stirring occasionally, until the vegetables soften and turn translucent, about 3 to 4 minutes. Add the minced garlic and cook for 30 seconds until fragrant.
06 - Add the ketchup, tomato paste, yellow mustard, smoked paprika, Worcestershire sauce, and chili powder if using. Stir thoroughly to combine all the seasonings with the aromatics.
07 - Pour in the beef broth and bring to a gentle simmer. Let it bubble for 2 minutes so the flavors meld together.
08 - Return the smashed patties to the skillet. Break them into bite-size pieces with your spatula and fold them into the sauce. Continue cooking for 2 to 3 minutes until the mixture thickens slightly and coats the beef evenly.
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 to trap heat and melt the cheese completely.
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 and lightly crisp.
11 - Spoon a generous portion of the cheesy beef mixture onto the bottom half of each toasted bun. Top with pickle chips, shredded lettuce, and tomato slices as desired. Cap with the top bun and serve immediately while hot.