1. In a bowl, gently mix one cup flour with mashed potatoes. Use your hands to knead the dough, adding the remaining quarter-cup flour gradually until the dough becomes soft and fluffy. Form into a ball and place in freezer for half an hour.
2. Once fully chilled, cut dough into four pieces. Roll each piece with your hands into a thin log, about three-quarter inches thick and 12 inches long. Cut into three-quarter-inch pieces, or to whatever size you like. They should resemble small pillows. Refreeze gnocchi until ready to cook.
3. Bring a large pot of generously salted water to boil. Drop gnocchi into water and boil for about three to four minutes. Use a mesh spider strainer to gently remove gnocchi. Top with sauce and shaved Parmesan, if using, and serve.