Wash the potatoes, and cook until tender in a pot with the caraway seeds. Drain the potatoes and leave them in the pot with lid on for a few minutes to steam them. Peel while still hot. Press the potatoes through a potato ricer, and allow to cool for some 30 minutes.
Separate the eggs; the whites may be used for another recipe. Add the yolks to the potatoes, and mix to combine. Blend the flour and cornstarch, and sift it onto the potatoes. Knead in gently, season with salt and mace, and blend.
Working on the floured surface, take one tablespoon of dough at the time, and roll it to a 2-inch long noodle approximately the thickness of a finger. The ends should be tapered. Make the noodles one by one until you have used up all of the dough.
Fill a large pot of water, bring it to a boil, and add two or three pinches of salt. Add the Schupfnudeln, and cook for a few minutes at low heat until they float to the surface. Remove from the pot with a slotted spoon, and drain on paper towels. Heat the oil and butter in a large pan, at moderate heat, fry the dumplings on all sides until golden brown. Season with salt and pepper.