Preheat the oven to 350F. Butter the bottom and sides of an 8x8 baking dish. Pour the thawed potatoes into the bettered dish. In a medium bowl, whisk together the eggs, milk, salt, and pepper. Pour the eggs over the potatoes. Sprinkle the cheese evenly over the casserole. Bake, uncovered, for 30-35 minutes. Allow to cool for 10 minutes before serving.
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