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Divide the onions into 4 individual mounds on a rimmed baking sheet. Form the beef into 4 loose balls. Place the beef balls on top of the onion mounds and flatten the beef firmly (use the palm of your hand) so the onion adheres to the beef. The patties should be 4 inches in diameter. Season the beef generously with salt and pepper.
Melt the butter with the oil in a 12-inch skillet over medium heat. Using a large spatula, place the patties in 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 and cook for about 2 minutes, until the second side is well browned.
Place 1 or 2 slices of cheese on each burger and let melt. Top the top buns with mayonnaise, mustard and pickles and place each burger on a bottom bun. Serve immediately.
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