Lay the thick-cut bacon in a large skillet over medium heat and cook until well rendered and crisp, 8–10 minutes; transfer to paper towels and pour off all but 2 tbsp of the fat.
Rinse and dry the iceberg lettuce leaves; set aside.
Split the hamburger buns; melt the unsalted butter in the skillet with 1 tbsp reserved fat and toast the cut sides until golden, 1–2 minutes. Set the toasted bottoms and tops aside.
Divide the ground beef (80/20) into 4 equal portions (about 5 oz each), gently form 4 1/2-inch patties with a shallow dimple in the center, and season both sides evenly with the kosher salt and black pepper.
Return the skillet to medium-high with a thin film of reserved fat; if the surface looks dry, add the neutral oil. Sear the patties without moving until deeply browned, 3–4 minutes.
Flip, top each with the American cheese slices, and cook 2–3 minutes more until the cheese melts and the centers reach your target doneness (juices run slightly rosy for medium, 135–140°F; firm and no pink for well done, 160°F). Transfer to a plate to rest 2 minutes.
Build the burgers: Thinly slice the yellow onion and cut the tomato into rounds; spread the ketchup and yellow mustard on the toasted bottoms, add the dill pickle chips plus a few rings and slices, set a patty on each with 2 strips, place a leaf on each top, spread the mayonnaise on the cut sides, and cap. Serve immediately.