Line a baking sheet with parchment paper.

Combine the water, butter, and salt in a large, heavy pot and bring to a boil. Remove from the heat, add the flour, and mix with a wooden spatula until combined. Let the dough sit until cool enough to handle, about 5 minutes. Knead the dough until smooth, about 1 minute. Place half of the dough in a piping bag fitted with a large open star tip. Pipe 4-inch-long churros onto the prepared baking sheet. Repeat with the remaining dough.

Combine the sugar and cinnamon on a large platter. Set aside.

Meanwhile, heat 4 to 5 inches of vegetable oil in a large Dutch oven until it registers 365 degrees F on a deep-fry thermometer. Add the churros in batches of three and fry, flipping once, until deep golden brown all over, about 4 minutes. Using a slotted spoon, transfer the churros to a paper towel–lined baking sheet to drain.

Roll the churros in the cinnamon-sugar mixture. Serve immediately.