01 - Place a large cast-iron skillet or griddle over medium-high heat and allow it to get ripping hot.
02 - Divide the ground beef into 4 loosely packed balls, being careful not to overwork the meat.
03 - Once the skillet is screaming hot, set the beef balls in the pan. Press down firmly with a sturdy spatula to flatten into thin patties with jagged, irregular edges. Season the top side with salt and pepper.
04 - Let the patties sit undisturbed for about 2 minutes until the edges turn deeply browned and crispy. Flip and cook another 1 to 2 minutes. Remove the patties and set them aside on a plate.
05 - Lower the heat to medium. Toss the chopped onion, bell pepper, and a generous pinch of salt into the same pan. Sauté until the vegetables soften and turn translucent, about 3 to 4 minutes. Add the garlic and stir for another 30 seconds until fragrant.
06 - Stir in the ketchup, tomato paste, yellow mustard, smoked paprika, Worcestershire sauce, and chili powder if using. Mix thoroughly until everything is well combined.
07 - Pour in the beef broth and let the mixture simmer for 2 minutes so the flavors come together.
08 - Return the smashed patties to the pan, breaking them into chunks with your spatula. Toss everything together and cook for 2 to 3 minutes until the sauce thickens slightly and clings to the beef.
09 - Lay 1 slice of cheese over each mound of saucy beef. Cover the pan briefly with a lid or foil just until the cheese melts into gooey perfection.
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 and crisp.
11 - Spoon the cheesy beef mixture generously onto the bottom half of each toasted bun. Pile on pickles, shredded lettuce, and tomato slices as desired. Crown with the top bun and serve immediately while piping hot.