Combine water, vanilla, salt, butter and sugar together in a medium saucepan over medium-high heat and bring to a boil. When it boils reduce the heat to low.
Add the flour all at once into the butter mixture and use a wooden spoon to stir vigorously until the flour is completely incorporated and a thick dough clumps into a ball, about 45 to 60 seconds. Keep stirring pushing the dough against the bottom of the pan and the sides for about 60 seconds.
Remove from the heat and transfer to the bowl of a stand mixer fitted with the paddle attachment. If you are using an electric mixer, transfer the dough to a large size mixing bowl. Allow the mixture to cool for about 1-2 minutes. Alternatively, you can incorporate the eggs by hand instead of using an electric mixer if preferred.
With the mixer on low speed, add the eggs, one at a time, scraping the sides of the mixing bowl as needed. Mix until the eggs are completely incorporated and the dough looks thick, glossy and smooth. Although it’s a thick dough, it should pull away and fall easily off the beaters when you lift them.
Let the dough cool (warm to room temperature is fine), then transfer to a piping bag fitted with a large star-shape piping tip.
Meanwhile, mix the cinnamon sugar in a shallow bowl and set aside.
In a Dutch oven or large saucepan heat the oil to around 350°F to a depth of about 2 inches.
While the oil heats up, line a baking sheet pan with paper towels. Set it near the pot of oil and place the cinnamon sugar right next to it.
To fry the churros, using a piping bag fitted with a large star tip, pipe churro dough directly into the hot oil, snipping the dough with scissors or kitchen shears at about 6-inch intervals. It’s best to only fry 3 - 4 churros at once so they have room and don’t touch.
Fry the churros until golden brown and crispy, about 2-3 minutes, flipping them so they get golden on all sides. Repeat with the remaining dough working in small batches.
Transfer the cooked churros to the prepared sheet pan and allow them to drain for about a minute. Roll the hot churros in the cinnamon sugar. Alternatively, you can spoon the cinnamon sugar over the hot churros.
Serve warm with the chocolate sauce.