In a small sauce pan over medium heat, melt butter and blend in flour. Let sit for a minute. Add all of cold milk, stirring with a whisk. Add seasonings. Cook sauce on low until smooth and boiling, stirring occasionally with a whisk. Reduce heat and stir in cheese.
Place half of the sliced potatoes in a lightly greased 8in. x 8in. baking dish. Pour half of cheese sauce over potatoes. Repeat with second layer of potatoes and cheese sauce. Sprinkle the remaining cheese on top. Top with some paprika for color.