Place potatoes in a large heavy saucepan and cover by 1 inch with cold water. Bring to a boil over high heat and cook until the potatoes are tender to the tines of a fork, 15-20 minutes. Drain in a colander and let cool slightly.
When they are cool enough to handle, peel the potatoes and rice or mash them, taking care to not leave any large pieces or chunks. Turn them out onto a lightly floured surface, shape into a mound, and let cool slightly so they are still warm but can be kneaded by hand.
Make a well in the center of the potatoes and pour in the eggs. Add the flour to the well, then add the cheese and season with the nutmeg, 2 teaspoons of salt, and a few grinds of pepper. Knead the mixture with a fork and then by hand, just until the ingredients are seamlessly integrated and come together in a dough.
Dust your hands with flour, and if necessary, reflour the work surface. Divide the dough into 6 pieces. Working with one piece at a time, roll it out into a rope about ½ inch in diameter. Use a sharp knife to cut each rope into 1 inch segments and transfer to a rice-flour-dusted baking sheet.
The gnocchi can be refrigerated for up to 1 day or frozen for up to 2 months.