Put the potatoes in a pot with cold water to cover, add 1/2 teaspoon of the salt, and bring to a boil. Boil gently for about 30 minutes, until very tender; be sure the potatoes are always covered with water during cooking. Drain the potatoes.
When they are cool enough to handle, peel the potatoes, cut into chunks, and push through a food mill or a ricer; or use an electric mixer to puree them.
Combine the milk, the remaining 1/4 teaspoon salt, the pepper, and butter in a heavy saucepan and bring to a boil. Remove from the heat and add all the flour at once, working the mixture with a wooden spoon until the mixture forms a ball. Return to the stove and cook for 30 seconds over low heat, stirring the mixture, which will become a shiny, homogeneous mass. Transfer to a bowl and let cool for 5 minutes.
Add the eggs one at a time to the dough, beating well with a whisk after each addition, then stir in the potatoes. Alternatively, transfer the dough to a food processor and, with the motor running, add the eggs. Process for 15 to 20 seconds, then combine in a bowl with the mashed potatoes.
Preheat the oven to 160 degrees.
Heat 1 1/2 to 2 inches of oil to about 350°F in a deep 10- to 12-inch skillet. Spoon 1 tablespoon of the dough at a time into the oil, pushing it out of the spoon with your finger; cook 10 to 15 pieces at a time. Cook for 8 to 10 minutes, turning the potatoes in the oil to brown them evenly on all sides. As soon as the first batch is done, remove with a slotted spoon and place on a tray lined with paper towels. Keep hot in the oven while you cook the remaining potatoes. Sprinkle lightly with salt and serve. (If the potatoes sit too long, they will lose their delicious crispness.)
Copyright © 2011 by Jacques Pépin. Used by permission of Houghton Mifflin Harcourt. All rights reserved.
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