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.
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.
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.
Make pâte à choux:
Bring water, butter, salt, pepper, and nutmeg to a boil in a 1-quart heavy saucepan over high heat, then reduce heat to moderate.
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.
Form and fry potatoes:
Put oven rack in middle position and preheat oven to 200°F.
Heat 2 inches oil in a 5- to 6-quart heavy pot over moderately high heat until thermometer registers 370°F.
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.
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.
• Potato batter can be made, but not formed or fried, 1 day ahead and chilled in pastry bag, with tip covered.
• 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 400°F oven until heated through and slightly crisp, about 5 minutes.