Melt the butter with the oil in a 12-inch skillet over medium heat. Using a large spatula, transfer the patties to the skillet, onion side down. Cook for 6-8 minutes, until the onions turn a deep golden brown and begin to crisp around the edges. Flip the burgers, then increase the heat to high and cook until well browned on the second side, about 2 minutes. Add 1 or 2 slices of cheese to each burger and allow to melt. Add mayo, mustard and pickles to the top buns, then place each burger on a bottom buns. Serve immediately.
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