Using a chef's knife or mandoline, cut the onions as thinly as possible. Set aside.
Portion the meat
Divide the ground beef into 4 equal balls (about 4 oz each). Try not to overpack the meat.
Heat the pan
Heat a cast iron skillet or flat-top griddle over medium-high heat until very hot (about 400-425°F).
Start the burgers
Place the beef balls on the hot skillet or griddle, leaving room between each. Immediately top each ball with a generous handful of sliced onions.
Season and smash. Sprinkle each mound with kosher salt and black pepper. Using a stiff spatula or burger press, smash each ball into a thin patty, about ¼-1/3 inch thick. Press firmly once and don't press again.
Cook the first side. Let the patties cook undisturbed until the edges of the onions and meat are browned and crisp, about 2-3 minutes.
Flip, add cheese, and steam buns. Slide a thin metal spatula under each patty, scraping up any browned bits, and flip so the onions are now touching the pan. Immediately top each patty with a slice of American cheese. Stack the bun tops, then the bottoms, cut-side down, on top of each patty to steam.
Finish cooking. Cook another 2-3 minutes, until the cheese is melted, the onions are soft and browned, and the patties are cooked through.
Build and serve
Transfer each patty and its steamed bottom bun to a plate. Add yellow mustard and dill pickle chips. Top with the bun lid and serve immediately. For double burgers, stack two patties on one bun.
NOTES
Using lean meat: You can still make these with leaner meat. Just don't smash the patties paper-thin. Leave them slightly thicker to keep them from drying out.Smash once only: Press the patties flat immediately after they hit the hot pan, then stop smashing. Pressing again later forces out fat and juices. Pan choice: A cast-iron skillet or flat-top griddle works best. Avoid nonstick for high-heat searing and crust development.Buns: Steaming the buns over the patties is part of the style. If you prefer extra texture, briefly toast the cut sides on the hot surface after steaming.Onion thickness: Slice onions paper-thin. If they're too thick, they won't soften as needed or stick to the patties.
Nutrition information is automatically calculated, so should only be used as an approximation.