In a heavy-bottomed saucepan bring water, unsalted butter, sugar, and salt to a low boil just long enough to melt the butter.
Add in the flour and mix with a rubber spatula until a thick dough forms.
Add the dough to a mixing bowl or bowl of a stand mixer and let cool for 5 minutes.
Using a whisk attachment, add egg and vanilla and mix until a looser dough forms. (It will resemble a pate a choux.)
Add your piping tip to the piping bag and cut off the opening at the end so that the dough will clear the tip.
Preheat vegetable oil in skillet.
Pipe churros in 5-6-inch-long strips of dough into the hot oil using a knife to cut off the end.
Fry on all sides about 3-5 mins, until golden brown.
Drain on paper towels and toss in cinnamon sugar.
To make the chocolate sauce.