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Heat butter in nonstick skillet over medium heat.
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Add mushrooms and onion; cook and stir 4 minutes or until mushrooms have softened. Cool completely.
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Mix ground beef.
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Measure twelve (1/4 cup) portions of beef. Shape into thin 4-inch round patties.
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Place about 1 tablespoon each of the mushroom mixture and cheese in center of each of 6 patties.
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Top with remaining hamburger patties, pinching edges to seal filling. If necessary, lightly flatten with spatula.
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Grill over medium heat 4 to 6 minutes per side or until burgers are cooked through.
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Serve burgers on rolls with lettuce, tomato, onion and ketchup.
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Enjoy!