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Bring a pot of water to a boil. Carefully add the potatoes to the pot and boil for 6 minutes.
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Drain the potatoes and rise with cold water until cool enough to handle.
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Grate the potatoes and add the grated potatoes to a medium sized bowl.
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Add the flour, egg, butter, cheese, salt, and pepper to the bowl and mix until everything is well combined.
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Use a greased 1/3 cup measuring cup to portion out the mixture and form into patties with your hands.