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Peel potatoes and cut into 1/2-inch cubes.
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Rinse with cold water.
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Drain.
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Pat potatoes dry with kitchen towels.
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Pour oil into heavy deep skillet to depth of 3/4-inch.
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Heat over medium-high heat until thermometer registers 375ºF.
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Working in batches, add potatoes to skillet; cook until light golden, about 15 minutes.
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Using slotted spoon, transfer potatoes to paper towels; cool.
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Melt 1 tablespoon butter in heavy large skillet over medium-high heat.
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Add onions and paprika and saute until onions are golden, about 5 minutes. (Can be prepared 8 hours ahead. Cover separately and keep at room temperature).
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Preheat oven to 400ºF.
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Melt remaining 1 tablespoon butter in skillet with sauteed onions over medium-high heat.
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Add potatoes and saute until golden brown, about 3 minutes.
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Season mixture to taste with salt and pepper.
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Spread mixture on heavy large baking sheet.
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Bake until potatoes are cooked through and crisp, about 15 minutes.