Season ground beef, form into 4 patties and set aside.
Heat a medium skillet on high heat, add 1 tablespoon oil and 1 tablespoon butter, and when butter is melted and lightly brown, add the onions and cook for 5 minutes. Then lower heat to medium, add a pinch of salt and cook additional 5 minutes. Set aside.
Heat a large skillet on high heat, add oil and when just reaching the smoking point, add the beef patties and, depending how you like them, cook 2-3 minutes each side, or longer if wanted more well cooked. Set aside.
Top 4 of the slices of bread each with some onions, a slice of cheese, cooked patty, another slice of cheese and finally a slice of bread. Slather each sandwich on top and bottom with the additional butter.
Then turn the heat to medium. Add the sandwiches. Cook for 3-4 minutes a side, or until the bread is golden browned and the cheese has melted. Slice in half diagonally and serve.
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