Pour about 2 1/2-inches of the oil into a saucepan, and heat it until it registers 350° on a deep-frying thermometer. Scoop out about 2 teaspoons of dough, and, with your index finger, push the dough to the far edge of the spoon, and let it drop into the hot oil. (Be sure to position your spoon very close to the surface of the hot oil to prevent splashing.) Repeat, with the remaining dough as quickly as you can; cooking about twelve potato balls at a time for 8 to 9 minutes, until the dauphine are well puffed, well browned, and cooked through. Remove with a slotted spoon, and drain on a wire rack. Serve hot.