In a small sauce pan, melt butter and blend in flour. Let it sit for a minute.
Add all of cold milk, stirring with a whisk and season with salt and cayenne. Cook sauce on low until smooth and boiling, stirring occasionally with a whisk.
Reduce the heat and stir in the sharp cheddar cheese.
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.
Finally top the potatoes with some paprika for color.