These burgers cook quickly, so make sure your buns are toasted and ready to go. Smear some mayo on each toasted bottom bun and top with iceberg lettuce and a few pickle chips. Set aside.
Preheat a large dry stainless steel skillet or flat top over high heat for 2 minutes. Alternatively, you can use a cast iron skillet.
Working in batches, place two balls of ground beef in the skillet and press firmly with the bottom of a saucepan or a large heavy spatula until they are very thin and slightly wider than your bun. Season generously with salt and pepper. Be careful not to crowd the pan.
Cook the patties until they are well browned and the tops are beginning to turn pale pink/gray in spots, about 1 minute. Using a bench scraper or a heavy metal spatula, carefully scrape the patties from the pan, making sure to get all of the browned bits.
Flip and immediately top each patty with a slice of cheese and stack one patty on top of the other. Transfer to a large plate and cover loosely with foil. Keep warm while you prepare the other burgers.
Arrange the smashed burgers on top of the prepared buns. Top each burger with a hefty spoonful of Balsamic Onion Jam and close your burgers. Serve right away with French fries and ketchup on the side, if desired.