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Preheat oven to 350 degrees.
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Wash and quarter the potatoes. Place in a saucepan, cover with boiling water, and cook until tender. Drain and shred coarsley with a grater.
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In a bowl, combine shredded potatoes with sour cream, scallions, 2/3 cup sharp Cheddar cheese, salt, and pepper. Mix well and transfer to a shallow baking dish or pie plate (9-10 inches).
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Sprinkle remaining cheese over top. Dust with paprika.
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Bake, uncovered, at 350 degrees for about 40 minutes, or until golden.
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(If you would like to make this ahead of time, just add 10 minutes or so to the baking time if the unbaked potatoes are chilled.).