2 1/4 pounds baking potatoes, peeled and cut into 2-inch chunks
1 large egg, beaten
1 tablespoon unsalted butter
2 tablespoons nonfat dry milk
2 tablespoons freshly grated Parmigiano-Reggiano cheese
1/2 cup all-purpose flour
Pinch of freshly grated nutmeg
Vegetable oil, for frying
Put the potatoes in a large saucepan and cover with water. Add a large pinch of salt and bring to a boil. Simmer over moderate heat until tender, about 20 minutes. Drain the potatoes and return them to the saucepan. Cook for 1 minute over high heat, shaking the pan frequently to dry out the potatoes.
Pass the potatoes through a ricer into a large bowl. Stir in the egg, butter, dry milk, cheese, flour and nutmeg; season with salt. Using floured hands, roll the potato mixture into 1-inch balls; you should have about 60.
Preheat the oven to 350°. In a large nonstick skillet, heat 1/2 inch of vegetable oil until shimmering. Working in batches of about 12, fry the potato balls over moderately high heat until they are browned on 3 sides, 2 to 3 minutes per side. Drain on paper towels, season lightly with salt and transfer the potato balls to a large rimmed baking sheet. Repeat with the remaining balls.
When all of the puffs are fried, reheat them in the oven for about 10 minutes. Serve at once.
Make Ahead The recipe can be prepared through Step 2 and refrigerated overnight. Bring the potato balls to room temperature before frying.