Turn dough out onto a lightly floured surface. Knead until dough is smooth, 10 to 15 minutes. (Alternatively, fit a mixer with a dough hook, and knead 8 to 10 minutes.) Cover dough with plastic, and let stand 30 to 60 minutes.

Divide dough into 8 pieces. Using a rolling pin, flatten 1 piece, rolling from the center outward, easing the pressure when the pin is close to the edge, until slightly thinner than the widest setting on a pasta machine. Dust lightly with flour, then feed through a pasta machine on the widest setting (#1), supporting both ends of the sheet with your palms to keep it flat; repeat twice. Turn dial to next narrower setting. Pass dough through twice. Continue to roll dough twice through each ever-finer setting, until thin (#5). Repeat with rest of pieces.

With a fluted pastry cutting wheel, cut each sheet of dough into strips that are 20 inches long and 1 inch wide.

Heat vegetable oil in a medium saucepan until it registers 350 degrees. Wrap end of 1 strip of dough around index and middle fingers, pinching end to create a loop of dough with a long tail. Wrap tail around 3 fingers, then around 4 fingers. Pinch end against spiral. Gently drop spiral into hot oil, and cook, turning once, until golden brown and puffed, about 2 minutes. Transfer to paper towels to drain. Repeat.