Preheat oven to 400 degrees.

Place 1 tbsp butter in a .5 quart oven-safe dish. Place in oven while it's preheating, and allow butter to melt. Meanwhile, peel and slice potatoes into thin circles.

Once butter is melted, coat the dish in butter, and place a layer of thinly-sliced potatoes on the bottom of the dish. Sprinkle on 1/3 of the Parmesan cheese, and repeat three layers.

In a small saucepan, melt 2 tbsp butter over medium-heat. Sprinkle in flour, and whisk quickly to avoid any lumps. Add in milk, whisking vigorously, until it starts to thicken. Stir in cheese and remove from heat.

Pour cheese sauce over potato dish. Bake on the bottom rack in preheated oven for 60 - 80 minutes, until potatoes are tender and cheese is golden brown.