Set up ice bath with 6 cups ice and 6 cups water near boiling water. Make well in center of potatoes and sprinkle all over with flour, using all the flour. Place egg and salt in center of well and using a fork, stir into flour and potatoes, just like making normal pasta. Once egg is mixed in, bring dough together, kneading gently until a ball is formed. Knead gently another 4 minutes until ball is dry to touch.
Flick pieces off of fork or concave side of cheese grater until dowel is finished.
Meanwhile, continue with remaining dough, forming dowels, cutting into 1-inch pieces and flicking off of fork. As gnocchi float to top of boiling water, remove them to ice bath. Continue until all have been cooled off. Let sit several minutes in bath and drain from ice and water.