01 - Set 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 - Place the beef balls onto the hot skillet and smash each one firmly with a metal spatula to form thin patties with jagged, rough edges. Season the top side with salt and pepper.
04 - Let the patties sear undisturbed for about 2 minutes until the edges are deeply crispy and browned. Flip and cook for another 1 to 2 minutes, then remove and set aside.
05 - Reduce the heat to medium. Add the chopped onion, bell pepper, and a pinch of salt to the same skillet. Sauté until the vegetables are softened, about 3 to 4 minutes. Add the minced garlic and cook 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 to combine all the flavors.
07 - Pour in the beef broth and let the sauce simmer for 2 minutes so the flavors meld together.
08 - Return the smashed beef 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 to trap the heat and melt the cheese until gooey.
10 - While the cheese melts, spread butter on the hamburger buns and toast them in a separate skillet or on a griddle until golden brown and crispy.
11 - Spoon the cheesy beef mixture generously onto the bottom half of each toasted bun. Top with dill pickle chips, shredded lettuce, and sliced tomato as desired. Cap with the top bun and serve immediately while hot.