In medium saucepan, combine butter and water. Bring to a boil; add salt and remove from heat. Add flour all at once; beat with wooden spoon. Return to heat; beat with wooden spoon for 2 minutes. Remove from heat; let cool.
Beat in an egg one at a time. Add vanilla and continue beating until mixture is satiny. Press mixture through fluted tip pastry bag or cookie press, 1/2-inch wide opening.
With wet scissors, cut into 2-inch strips as it (carefully) drops in oil heated to 350°F. Fry for 2 minutes on each side. Do a few at a time. Drain; roll in cinnamon sugar mixture.