If your butcher cannot shave the ribeye, freeze the beef for 2 hours and slice on a mandolin for paper-thin results.
Cook the meat over medium-high heat and don't overcrowd the pan. Shaved steak cooks in minutes and needs high heat to brown rather than steam.
Let the liquid reduce fully before building the sliders so the rolls don't get soggy.
These are best eaten immediately while the cheese is still melted and the rolls are warm and slightly toasted on top.