Preheat the oven to 350°F. Grease a 2-quart baking dish with 1 teaspoon of the butter.
Put the potatoes in a large mixing bowl and add the salt and white pepper. Toss to season evenly. Arrange a layer of potatoes on the bottom of the prepared baking dish and sprinkle with 2 teaspoons of the flour. Dot with a tablespoon of the remaining butter, then sprinkle with 1/2 cup of each of the cheeses. Repeat the process until all the potatoes, butter, flour, and cheeses are used, ending with the cheeses. Pour in the milk.
Bake until golden brown and bubbly, about 1 hour. Remove from the oven and serve hot.
Yield: about 8 servings