Preheat oven to 325 degrees F (165 degrees C).
Arrange thinly sliced potatoes in a 9×13-inch baking dish.
Layer butter slices on top of potatoes. Season with salt and black pepper.
Pour half-and-half evenly over potato mixture.
Bake in preheated oven until sauce has thickened and potatoes are tender, 45 to 60 minutes.
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