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1
Make duchesse potatoes:
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Peel potatoes and cut into 1-inch pieces. Cover potatoes with cold salted water by 1 inch in a 2-quart pot, then simmer, uncovered, until tender, about 15 minutes.
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Drain potatoes in a colander and return to pot. Dry potatoes by shaking pot over low heat until all moisture is evaporated and a film begins to appear on bottom of pot, about 2 minutes.
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4
Force potatoes through ricer into a bowl. Add butter, whole egg and yolk, salt, and pepper and stir with a wooden spoon until very smooth. Keep potato mixture warm, covered.
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5
Make pate a choux:
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Bring water, butter, salt, pepper, and nutmeg to a boil in a 1-quart heavy saucepan over high heat, then reduce heat to moderate.
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Add flour all at once and stir briskly with a wooden spoon until mixture pulls away from side of pan, 1 to 2 minutes. Remove from heat and cool slightly, about 3 minutes. Add eggs 1 at a time, stirring well after each addition. Add potato mixture and stir until combined well. Transfer mixture to pastry bag.
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8
Form and fry potatoes:
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9
Put oven rack in middle position and preheat oven to 200u00b0F.
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Heat 2 inches oil in a 5- to 6-quart heavy pot over moderately high heat until thermometer registers 370u00b0F.
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Resting metal tip of pastry bag on edge of pot, pipe 8 (2-inch) lengths of potato mixture directly into oil (use caution when piping into hot oil), using a small knife or kitchen shears to cut off each length of dough at tip of bag. Fry potatoes, turning over once with a slotted spoon, until crisp, golden, and cooked through, 2 to 3 minutes. Transfer to paper towels to drain briefly. Fry remaining potato mixture in batches in same manner.
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Transfer potatoes as fried and drained to a metal rack set in a large shallow baking pan in oven to keep them crisp and warm until ready to serve.
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Cooks' notes:
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Potato batter can be made, but not formed or fried, 1 day ahead and chilled in pastry bag, with tip covered.
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15
Potatoes can be fried 2 hours ahead and kept at room temperature, on rack in baking pan and loosely covered with paper towels. Remove paper towels and reheat in a 400u00b0F oven until heated through and slightly crisp, about 5 minutes.