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In a small sauce pan, melt butter and blend in flour. Let sit for a minute. Add all of cold milk, stirring with a whisk. Season with salt and cayenne.
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Cook sauce on low until smooth and boiling, stirring occasionally with a whisk. Reduce heat and stir in cheese.
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Place a half of the sliced potatoes in a lightly greased one quart casserole dish. Pour half of cheese sauce over potatoes. Repeat with second layer of potatoes and cheese sauce. Sprinkle the remaining cheese on top.
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Top with some paprika for color.
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Bake uncovered for about 1 hour at 350°F.