3 pounds of potatoes, peeled and quartered
Bring 4 quarts of water to a boil in a 6- to 8-quart pot and drop in the potatoes. Boil briskly, uncovered, until they are soft enough to be easily pierced with a fork. Drain them thoroughly in a large sieve and force them through a ricer or mash them in a bowl with a fork. Beat in the egg, ½ cup of flour and salt, and continue to beat vigorously until the mixture is smooth and dense enough to hold its shape almost solidly in a spoon. (If the mixture seems too fluid, beat in the remaining flour, a tablespoon at a time.)
Melt 2 tablespoons of butter in a heavy 10- to 12-inch skillet set over high heat. When the foam has almost subsided add 6 or 8 of the patties and brown them 3 to 5 minutes on each side, turning them over carefully with a large spatula. Transfer the patties to a serving platter and cover them loosely with foil to keep them warm while you fry the rest of the patties, adding more butter to the pan as needed.