Grate the potatoes, cooked and peeled the day before, into a container. Knead with egg, salt, nutmeg and flour to a firm dough.
Place the dough on a floured baking sheet and cut small rolls of just under 1 cm in diameter into 4 cm long pieces.
In a large saucepan, bring enough salted water to a boil. Let the Schupfnudeln cook in it for 10 minutes until fork-tender.
Drain the Schupfnudeln well.
Heat butter in a frying pan. Fry half of the Schupfnudeln in it for 10 minutes until golden brown.
Turn carefully once more.
Remove the Schupfnudeln and keep warm on a warmed plate until the remaining Schupfnudeln are ready.