Preheat the oven to 400 degrees F. Butter a 9-by-13-inch baking dish with the butter.
Dice the potatoes and place in the prepared baking dish.
Combine the cream and milk in a bowl. Add the flour, salt and pepper. Whisk together until the flour is incorporated. Pour the cream mixture over the top of the potatoes.
Cover with foil and bake for 20 minutes. Uncover and top with the cheeses. Bake for an additional 30 minutes. Remove from the oven and allow to sit for 5 minutes. Sprinkle over the chives and serve.
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