Prepare the grill for direct grilling over high heat, about 700°F grill grate temperature.
Slice the red onion into ¾ inch thick slices. Oil both sides and season liberally with salt. Reserve.
Slice the pretzel rolls. Pour oil into a dessert plate, then dip the cut sides of each roll into the oil for an even coating. Season the oiled side with a little salt. Reserve.
Form the ground beef into patties 1 inch larger in diameter than the rolls and about ¾ inch thick. Use care to work the ground beef as little as is necessary to maintain a desirable texture. Recess the center of the patties so that when the burgers plump up on the grill, they will turn out flat. The reason we form the patties 1 inch larger than the rolls is so that when they shrink on the grill, they do not become smaller than the rolls.
Brush each patty on all sides with olive oil and season with salt. The olive oil will help form a nice crust on the outside of the patty.
Grill the onion slices until translucent and soft, about 10 minutes. Remove from the grill, break the slices down into rings and reserve.
Grill the beef patties, turning once, 3 to 4 minutes per side. When you flip them, add a large ring of onion to the top of each patty, so it sits neatly in a circle. Add a small ring or two of onion inside the larger ring, also sitting neatly. Add the cheese on top of the onion. The cheese will melt, almost into a creamy sauce, and the onions will help hold it on top of the burger.
While the cheese is melting and the second side of the patties are cooking, lightly grill the rolls.
Gently remove the burgers when they are done and transfer directly onto the pretzel rolls. Skewer each burger to hold it together. Serve with at least six napkins per burger.
Watch these sliders being prepared and get a couple of grilling tips in this video shot at the Robb Report Car of the Year event in Napa.
