Bake the potatoes in a preheated 425° oven for about 50 minutes, or until they are soft, halve them lengthwise, and scoop the potato out of the shells with a spoon, reserving the shells for another use. Force the scooped out potato through a ricer or a food mill fitted with the medium disk into a large bowl.
In a saucepan combine 3 tablespoons water, the butter, the salt, and the nutmeg, bring the mixture to a boil, and stir in the flour all at once. Reduce the heat to moderate and beat the mixture vigorously with a wooden spoon for 3 minutes, or until the paste pulls away from the side of the pan and forms a ball. Remove the pan from the heat, add the egg, beating the mixture until it is smooth and shiny.
Add the potatoes and beat the mixture until it is combined well. The potato mixture may be prepared up to this point 1 day in advance and kept covered and chilled. In a deep fryer or large kettle heat 2 inches of the oil until it registers 340° on a deepfat thermometer. Transfer the potato mixture to a large pastry bag fitted with a 1/2 inch star tip and pipe eight 2 1/2 inch lengths, cutting them with kitchen shears or a small knife, directly into the oil. Fry the croquettes, turning them with a slotted spoon, for 3 minutes, or until they are crisp, golden, and cooked through, transfer them as they are fried to paper towels to drain, and sprinkle them with the salt. Make more croquettes in batches with the remaining potato mixture and transfer the drained croquettes to a rack set in a jellyroll pan (to prevent them from becoming soggy).
The croquettes may be made 2 hours in advance, kept covered loosely with paper towels at room temperature, and reheated on the rack in a preheated 400° oven for 5 minutes, or until they are heated through and crisp. If not making the croquettes in advance, keep them warm in a preheated 300° oven.