01 - Set a large cast-iron skillet or griddle over medium-high heat and allow it to get fully hot before cooking.
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. Press down firmly with a metal spatula to form thin patties with irregular, crispy edges. Season the top side with salt and pepper.
04 - Let the patties cook undisturbed for about 2 minutes until the edges are deeply browned and crisp. Flip and cook for another 1 to 2 minutes, then remove and set aside.
05 - Reduce the heat to medium. Add the chopped onion, diced bell pepper, and a pinch of salt to the same pan. Sauté until the vegetables are 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 let the mixture simmer for about 2 minutes so the flavors meld together.
08 - Return the smashed patties to the pan, breaking them into smaller pieces with the spatula. Fold the beef into the sauce and cook for 2 to 3 minutes until the mixture is slightly thickened and cohesive.
09 - Lay 1 slice of cheese over each portion of the beef mixture. Cover the pan briefly to allow the cheese to melt evenly over the top.
10 - While the cheese melts, spread butter on the cut sides of each hamburger bun. Toast in a separate skillet or on a griddle over medium heat until golden brown.
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. Place the top bun and serve immediately while hot.