1 1/2 pounds ground beef
Kosher salt and freshly ground black pepper, to taste
5 tbsp. canola oil
6 yellow onions, halved and thinly sliced
12 slices rye bread
12 thin slices cheddar, swiss, or American cheese
8 tbsp. unsalted butter, softened
Season the beef with salt and pepper. Divide meat into six 1/4"-thick patties that are slightly wider and longer than the bread.
Heat 2 tbsp. oil in a 12" cast-iron skillet over medium-high heat. Add the onions, season with salt and pepper, and cook, stirring occasionally, until softened and browned, about 12 minutes.
Transfer the onions to a bowl; wipe out skillet. Working in 3 batches, heat 1 tbsp. oil in skillet over high heat. Add 2 burger patties; cook, flipping once, until well browned, about 4 minutes total. Transfer patties to a plate.
Top each of 6 bread slices with some of the onions, a cheese slice, and a burger patty. Top each burger with a cheese slice and a piece of bread. Using a table knife, spread butter over the top and bottom of each sandwich.
Heat a 12" nonstick skillet over medium heat. Working in 3 batches, cook sandwiches, flipping once, until golden brown and hot, about 6 minutes.
The patties really do have to be 1/4 inch thin. They thicken when cooked and if too large makes this an unweildy sandwich. Always a cardinal sin