Pinch off a portion of the dough and make a ball about 4 cm / 1 1/2 inches in diameter by rolling between the palms of your hands. On a lightly floured work surface, roll out into a disc about 11 cm / 4 1/2 inches in diameter and 1.5 mm / 1/8 inch thick; if rolled too thin, it may not puff up. Shake off excess flour.
Heat oil in a deep fat fryer or saucepan to 190C/375F. Carefully drop a disc into the hot oil. It will rise to the surface and puff up immediately, either entirely or in several places. Remove with a slotted spatula and drain on paper towels. Since they cook in a few seconds, I fry one luchi at a time.