Heat a cast-iron griddle or large heavy skillet over medium-high until very hot, about 2 minutes, then lightly brush with vegetable oil.
Divide ground beef into 4 equal portions (do not form patties). Working in batches if needed, place portions on griddle and smash flat with a large diameter cup to form 4inch diameter patties (craggy edges are your friend).
Season liberally with salt and cook, undisturbed, until outer edges are brown, about 2 minutes.
Flip patties, season with salt, and place a slice of cheese on top of each patty.
Cook until cheese droops and burgers are medium-rare, about 1 minute. Layer two patties on top of one of another and place on top of a lightly toasted english muffin.
Top with infused 1,000 Island and finish with iceberg lettuce.