Heat 1 tablespoon of the oil in a large cast iron skillet over medium heat. Add the onion, season with some salt and pepper, and cook until golden, about 7 minutes. Put in a bowl and set aside. Wipe out the skillet and add another tablespoon of oil. Season the turkey patties with salt and pepper, and cook in the remaining oil until well browned, about 3 minutes per side. Remove from the skillet. Wipe out the pan.
Divide the onions among 4 bread slices, and top with a slice of cheese, a patty, another slice of cheese, and a slice of bread. Spread the top and bottom of the sandwiches with some butter. Heat the cast iron skillet over medium heat. Cook the sandwiches, in batches if needed, turning once, until lightly browned and the cheese melts, about 2 minutes per side. Halve the sandwiches and serve with cranberry sauce, if desired.
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