01 - Set a large cast-iron skillet or griddle over medium-high heat and allow it to get ripping hot.
02 - Gently 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 press down firmly with a sturdy spatula to flatten into thin patties with jagged, irregular edges. Season the top with salt and pepper.
04 - Let the patties cook without disturbing for about 2 minutes until the edges turn deeply browned and crisp. Flip each patty and cook for another 1 to 2 minutes, then remove from the pan and set aside.
05 - Lower the heat to medium. Add the chopped onion, diced bell pepper, and a pinch of salt to the same skillet. Sauté until the vegetables soften, about 3 to 4 minutes. Stir in the minced garlic and cook 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 aromatics.
07 - Pour in the beef broth and bring to a gentle simmer for about 2 minutes, allowing the flavors to come together.
08 - Return the smashed patties to the pan and break them apart with your spatula, folding the shredded beef into the sauce. Continue cooking for 2 to 3 minutes until the mixture thickens slightly.
09 - Lay one slice of cheese over each mound of the beef mixture. Cover the skillet with a lid briefly until the cheese melts into gooey perfection.
10 - While the cheese melts, butter the cut sides of the hamburger buns and toast them in a separate skillet or on the griddle until golden brown.
11 - Spoon the hot beef and cheese mixture generously onto the bottom half of each toasted bun. Top with pickle chips, shredded lettuce, and tomato slices as desired. Cap with the top bun and serve immediately while hot.