In a saucepan, melt the butter over medium heat. Stir in the flour and cook for 1-2 minutes.
Gradually whisk in the milk, and cook until the mixture thickens and bubbles. Remove from heat.
Stir in the salt, pepper, and half of the grated cheese until melted and smooth.
Layer half of the sliced potatoes in a greased baking dish. Pour half of the cheese sauce over the potatoes. Repeat with the remaining potatoes and cheese sauce.
Sprinkle the remaining cheese on top.
Cover with aluminum foil and bake for 30 minutes. Remove the foil and bake for an additional 30 minutes, or until the potatoes are tender and the top is golden brown.
Let it cool for a few minutes before serving.
Notes:
For a twist, try adding some chopped ham or bacon to the layers.