Toss the sliced onion with 1/2 teaspoon salt, rest it for 10 minutes and squeeze it firmly in a clean towel until no longer wet.
Heat a large steel griddle or cast-iron skillet over high heat and toast the buttered buns for 1 minute; move them to plates.
Set the cold beef balls on the hot surface and immediately mound one-quarter of the onions over each one.
Press each onion-topped ball firmly through parchment to 1/4 inch thick so the strands embed in the meat, then season with the remaining salt and pepper.
Cook untouched for 2 minutes until the beef edges brown; do not press the patties a second time.
Scrape under the patties, flip them onion-side down and cook for 2 to 3 minutes until the onions brown and the beef reaches 160°F.
Top each patty with American cheese for the final 30 seconds, then transfer to a bun with mustard and 3 pickle chips.
