In a medium saucepan of boiling water, cook the potato until tender, about 8 minutes; drain. Let cool slightly, then transfer to a large bowl. Mash the potato and then mash with the remaining ingredients to form a sticky dough.
Bring a large pot of salted water to a boil. Pat one-quarter of the spaetzle dough into a 3-inch square on a small cutting board with a handle, or on the back of a square cake pan. Using a moistened chef's knife, cut off 1/4-inch-thick strips of dough and scrape them into the boiling water; moisten the knife if it sticks to the dough. Boil the spaetzle for 30 seconds without stirring, then gently stir to separate the strips. Cook just until the spaetzle rises to the surface. Using a small strainer or a wire skimmer, transfer the spaetzle to a bowl of ice water. Return the water in the saucepan to a boil and cook the remaining spaetzle. Drain well, shaking off the excess water.