Stir together the sugar and cinnamon in a large bowl or shallow dish. Set aside.

In a large saucepan, bring the water, butter, sugar, and salt to a boil over medium-high heat. When it boils, immediately take the pan off the heat.

Using a wooden spoon, add all the flour at once, and stir hard until all the flour is incorporated, 30 to 60 seconds.

Return to the heat and cook, stirring, for 30 seconds. Scrape the mixture into a large mixing bowl or the bowl of a stand mixer fitted with a paddle attachment.

Mix at medium speed for 2 minutes to start cooling the mixture down. With the mixer running, add 3 eggs, one egg at a time, stopping to scrape down the bowl between each addition. Add in the vanilla. Mix until the dough is smooth and glossy and the eggs are completely incorporated. The dough should be thick but should fall slowly and steadily from the beaters when you lift them out of the bowl. If the dough is still clinging to the beaters, beat the remaining 1 egg and mix in a little at a time until the dough is the right consistency (you may not need the whole egg). Transfer the dough to a large piping bag fitted with a large closed star tip. I used an Ateco 846. (DO NOT use a plain round tip! The ridges are important to keep the churros from bursting open when frying.)

Fill a large pot with 2 inches of oil, insert a deep fry or candy thermometer, and heat to 400°F over medium heat. While the oil is heating, line a large baking sheet with paper towels.

Working carefully, pipe 3-5-inch-long strips of dough into the hot oil. (It's best to fry about three at a time.) Fry on both sides for 1 to 2 minutes or until golden brown. Remove the churros with tongs and allow to drain on the paper towels for about thirty seconds before placing in the cinnamon sugar. Toss in the sugar, tapping to remove any excess, and serve immediately.