When the grill is medium-hot, brush the grill grate with oil to keep the sliders from sticking. Place the sliders on the grill and cook for 4 minutes. Turn the sliders over with a spatula and cook for another 4 to 6 minutes, until medium-rare, or cook longer if you prefer the sliders more well done. For the last 2 minutes of cooking time, place 1/2-ounce Gruyere on the top of each burger and close the grill lid. Remove the sliders to a platter and cover with foil.
Slice the buns in half crosswise and toast the halves cut side down on the grill.