Heat a cast-iron skillet 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 and roll into smooth rounds (do not form patties). Working in batches if needed, place rounds of meet onto the hot skillet and smash flat with the back of the spatula until very thin (meat will shrink up as it cooks). Patties should be about 5" in diameter. Season liberally with seasoned salt and pepper and cook undisturbed, until outer edges are brown, about 4 minutes.
Flip patties, season with remaining seasoned salt and pepper, and allow to cook for an additional 2 minutes. Add one slice of cheese to each burger. Cook until cheese droops and burgers are medium-well, about 1 minute. Allow to rest while you toast the buns.
Reduce heat to medium. Brush inside of buns with melted butter and lay face down on the griddle to toast for about 2 minutes, rotating halfway through. Remove the buns and place one slice of cheese on the bottom of the bun.