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Slice onion, keeping slices whole. (Do not split layers apart)
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Slice buns in half making a top and bottom bun. Butter each half.
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Heat two skillets to medium heat over stove. (One for burgers and one for the rolls).
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Divide hamburger into 9 to 12 equal sections, depending upon desired size.
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Roll into hamburger balls then pat down down with a square lid, making the patty about 3" square (they should be very thin). Note: A small plastic container lid works great!
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Place an onion round on top.
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Spray skillet with cooking spray and place hamburger patties on top with onion side down. Cook 3 minutes and turn, cooking until hamburger is completely cooked and juices run clear.
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Melt cheese over hamburger.
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While hamburgers are cooking, brown buttered rolls in other skillet until a golden brown.
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Assemble burgers, adding pickles and desired condiments.
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Serve immediately.