Preheat oven to 425 degrees F (220 degrees C). Grease a 9×13-inch baking dish.
Arrange one layer of potatoes in the bottom of the prepared baking dish. Sprinkle the potatoes with salt and pepper, 3 tablespoons flour, and 2 tablespoons butter. Repeat layering 2 more times, until all of potatoes have been used. Slowly pour milk over the potatoes until the dish is 3/4 full of milk.
Bake until the milk comes to a boil (check after 15 minutes), then reduce heat to 375 degrees F (190 degrees C) and bake until potatoes are tender, 45 to 60 minutes more.
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