Shape the ground beef into 1½-inch patties (about 14) and sprinkle with the salt.
In a small bowl, combine the ketchup and mayonnaise.
Heat the olive oil in a large cast-iron skillet over medium heat. Working in batches, cook the patties 2 minutes per side, topping each with a small slice of American cheese after flipping.
Thread the patties onto skewers with the dill pickle chips, sliced plum tomato and lettuce. Serve with the ketchup-mayonnaise mixture.
