Add oil and 1 tablespoon of butter to a hot fry pan. Add the onions and sauté until lightly browned then set aside.
Form the ground beef into two elongated patties roughly in the shape of the rye bread and slightly larger (they will shrink). Cook the patties in the fry pan until done, about three minutes per side. Lightly salt each side. Remove them from the pan.
Add ½ tablespoon of butter to the pan. Place one slice of bread directly over the melted butter, then add two slices of cheese, and ¼ of the cooked onions, a cooked beef patty, more onion, two slices of cheese and another piece of bread.
Place a metal bowl upside down over the assemble sandwich. This is an important step. It will help melt the cheese and soften the bread. Cooked the sandwich for a minute or two until the bread begins to brown.
Carefully remove the bowl with a spatula and some tongs (it will be HOT). Add another ½ tablespoon of butter to the pan and flip the sandwich over on top of the melted butter. Carefully cover the sandwich with the bowl and cook for another minute or two. Enjoy.