Heat Oil: In a deep fryer or large pan, add about 2 inches of oil but no fuller than halfway up the sides. Heat over medium heat to 375°.
Measure flour and set aside
Bring water, butter, vanilla, sugar, and salt to a boil in a 3-qt. saucepan over medium-high heat, stirring occasionally.
Immediately remove from heat, and quickly stir in flour mixture all at once.
Return to heat and stir with a wooden spoon for 1 to 2 minutes, or until dough is smooth and forms a ball
Transfer dough to the bowl of an electric mixer and let cool 5 minutes.
Add eggs, 1 at a time, beating until mixture is smooth and glossy.
Prepare Cinnamon Sugar: whisk together ½ cup sugar and cinnamon in a shallow dish or pie plate, set aside.
Spoon dough into a pastry bag fitted with a closed rose tip (Wilton 1F or Ateco 846).
Carefully pipe dough into preheated oil, in 6-inch lengths. Use kitchen scissors or tongs to cut off dough from piping bag. Cook 2 or 3 churros at a time. Fry until golden brown, about 4 minutes per side.
Remove churros with tongs to a plate to cooling tray lined with paper towels. Roll churros in cinnamon sugar, and place on a cooling rack.
Repeat process with remaining dough.
Serve warm with dulce de leche or chocolate sauce for dipping if desired.