Make churros: In a large saucepan over medium heat, add water, butter, and sugar. Bring to a boil, then add vanilla. Turn off heat and add flour and salt. Stir with a wooden spoon until thickened, 30 seconds. Let mixture cool for 10 minutes.

To cooled mixture, using a hand mixer, beat in eggs one at a time until combined. Transfer mixture to a piping bag fitted with a large open star tip.

In a large pot over medium heat, add enough oil to come halfway up the sides and heat to 375 degrees. Holding the piping bag a few inches above the oil, carefully pipe churros into 6" long ropes. Use kitchen scissors to cut off dough from piping bag.

Fry until golden, 4 to 5 minutes, turning as necessary. Fry 3 to 4 churros at a time and let oil come back to 375 degrees before each batch. Remove churros with a slotted spoon or tongs and immediately roll churros in cinnamon sugar, then place on a cooling rack.