01 - Place a large cast-iron skillet or griddle over medium-high heat and allow it to get fully hot, approximately 3 to 4 minutes.
02 - Divide the ground beef into 4 loosely packed balls. Avoid overworking the meat to keep it tender.
03 - Place the beef balls onto the hot skillet. Press each one firmly with a sturdy metal spatula to form thin patties with rough, jagged edges. Season the top side with salt and pepper. Let them cook undisturbed for about 2 minutes until the edges turn deeply browned and crispy.
04 - Flip each patty and cook for another 1 to 2 minutes on the second side. Remove the patties from the skillet and set them aside on a plate.
05 - Reduce the heat to medium. Add the chopped onion, diced bell pepper, and a pinch of salt to the same skillet. Sauté until the vegetables have softened, about 3 to 4 minutes. Add the minced 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 all the seasonings with the vegetables.
07 - Pour in the beef broth and bring the mixture to a gentle simmer. Let it cook for about 2 minutes so the flavors meld together.
08 - Return the smashed beef patties to the skillet. Break them up into bite-size pieces using your spatula and stir everything together. Continue cooking for 2 to 3 minutes until the sauce 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 allow the cheese to melt completely.
10 - While the cheese melts, spread butter on the cut sides of each hamburger bun. Toast them in a separate skillet or on a griddle over medium heat until golden brown, about 1 minute per side.
11 - Spoon the hot cheesy beef mixture generously onto the bottom half of each toasted bun. Top with dill pickle chips, shredded lettuce, and sliced tomato as desired. Place the top bun on each and serve immediately while hot.