Divide the ground beef into four equal, loose balls; do not press or form patties at this stage.

In a small mixing bowl, whisk together the mayonnaise, ketchup, mustard, relish, garlic powder, onion powder, and paprika to make the smash sauce.

Heat a cast iron skillet or griddle over high heat until it begins to smoke, then add a pat of butter to the hot surface.

Place a beef ball on the hot skillet and immediately smash it flat with a sturdy spatula, pressing down firmly for 10-15 seconds to create a thin patty; season generously with salt and pepper.

Cook for 90 seconds, then scrape under the patty to release it, flip, and immediately place a slice of American cheese on top.

Continue cooking for another 60-90 seconds until the cheese is melted and the patty edges are crispy; remove and set aside, repeating with the remaining beef balls.

While the burgers cook, lightly butter the hamburger buns and toast them on the same skillet until golden brown.

Assemble the burgers by spreading smash sauce on the bottom bun, adding a patty with cheese, dill pickles, and sliced onion, then topping with the upper bun; serve immediately.