Scrub potatoes, cook unpeeled and peel while hot. Puree in a food mill or rub through a sieve. Add butter, 2 eggs, grated cheese and mix well. Season with salt and nutmeg to taste. Work flour into potatoes, a tablespoon or two at a time, until you can form croquettes-sausage-shaped rolls about 1½" in diameter and 2" to 3" long. Dip each roll in egg-water mixture and roll in breadcrumbs until well coated on all sides. Heat fat in deep fryer. When it registers 375°F on a fat thermometer, add croquettes, four or five at a time, and cook each batch until they are a deep golden brown. Drain on paper towel before serving. If you prefer not to deep-fry these, shape potato-flour mixture into hamburger-like patties and fry in I" hot fat. Drain on paper towel and serve.