Prepare a grill for medium heat. Divide the ground beef into 6 even pieces and shape each into a 1-inch-thick patty. Press in the center of each patty so it is slightly thinner than the edges. Sprinkle generously on both sides with salt and pepper. Lightly oil the grill grates.
Grill the burgers, flipping once, until well browned and medium rare, 6 to 7 minutes per side, topping with a slice of cheese in the last few minutes of grilling. Lightly brush the buns with oil and grill until lightly toasted. Put the burgers on the bottom buns and top with the lettuce, tomato, onions and top buns. Serve with ketchup and mustard on the side.
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