Remove burgers from refrigerator and allow to come to room temperature, about 20minutes; season burgers on both sides with salt and pepper.
2, 3-burger batches: In a large cast iron skillet, place 4 tablespoons vegetable oil and create 3 small piles of thinly sliced onions, about 2 tablespoons.
Place the 3 burgers on the3 piles of onions and use a burger press to smash burgers until about 1/2”thickness.
Cook burgers about 4minutes, until seared and browned; flip and add 1 slice of American cheese to each and cook another 3 to 4 minutes, until cheese melts and burger cooked to desired doneness.
Remove burgers from cast iron pan, clean and wipe out pan, and repeat process for remaining burgers.
In a separate cast iron pan, add butter and toast buns, toasting the extra bun bottom (the middle bun)on both sides for 30 to 45 seconds until golden brown.