01 - Set a large cast-iron skillet or griddle over medium-high heat until smoking hot.
02 - Divide the ground beef into 4 loosely packed balls, being careful not to overwork the meat.
03 - Place beef balls onto the hot skillet and press firmly with a metal spatula to flatten into thin patties with rough, jagged edges. Season the tops with salt and pepper.
04 - Let the patties sear undisturbed for about 2 minutes until the edges are deeply browned and crispy. Flip and cook 1 to 2 minutes more. Transfer to a plate and set aside.
05 - Reduce heat to medium. Add the chopped onion, bell pepper, and a pinch of salt to the same skillet. Sauté until softened, about 3 to 4 minutes. Add the garlic and stir 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.
07 - Pour in the beef broth and bring to a gentle simmer for 2 minutes to meld the flavors together.
08 - Return the smashed patties to the skillet, breaking them up with the spatula and folding them into the sauce. Cook for 2 to 3 minutes until the mixture is slightly thickened and cohesive.
09 - Lay 1 slice of cheese over each mound of the beef mixture. Cover the skillet briefly with a lid or foil until the cheese is fully melted.
10 - While the cheese melts, spread butter on the cut sides of each bun and toast in a separate skillet or on the griddle until golden brown.
11 - Spoon the cheesy beef mixture generously onto the bottom half of each toasted bun. Layer with pickle chips, shredded lettuce, and sliced tomato as desired. Cap with the top bun and serve immediately while hot.