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Melt butter over medium heat in a saucepan, incorporate the flour with a whisk. Cook for 2-3 minutes.
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Whisk the milk in slowly, stirring briskly, cook till starts to thicken.
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Slice the potatoes about an 1/8 inch thick with food processor or mandoline.
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Pour a little sauce in a casserole dish, spread it all over.
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Make a layer with the potatoes, then sprinkle on the Swiss cheese. Continue to make layers with potatoes sauce, cheese, salt and pepper, alternating between Swiss and Parmesan, end with parmesan cheese.
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When done press down some sauce should come up.
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Cover with with foil and cook for 40-60 minutes.
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When it is done a knife should insert easily.
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When it is done take off the foil and turn on the broiler, and broil till the gratin is browned.
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Rest for 10-20 minutes. Resist the urge to dig in or it will not be set.