Prepare the Dough: In a medium saucepan over medium heat, combine water, unsalted butter, 1 tablespoon granulated sugar, and salt. Bring the mixture to a boil.
Add Flour: Once boiling, add the flour all at once. Stir vigorously until the mixture forms a ball and pulls away from the sides of the saucepan.
Cool and Add Eggs: Remove the pan from the heat. Let the dough cool for about 5 minutes. Beat in the eggs one at a time, ensuring each egg is fully incorporated before adding the next. Stir in vanilla extract.
Heat the Oil: Pour vegetable oil into a large, heavy-bottomed pot to a depth of about 2 inches. Heat the oil to 350°F (175°C).
Pipe the Dough: Spoon the dough into a piping bag fitted with a large star tip. Pipe 1-inch pieces of dough onto a parchment-lined baking sheet.
Fry the Churro Bites: Use a knife or scissors to cut the dough into the hot oil. Fry the churro bites in batches, turning them occasionally until they are golden brown (about 2-3 minutes per batch).
Drain and Coat: Use a slotted spoon to remove churro bites from the oil and place them on a paper towel-lined plate to drain. While still warm, roll the churro bites in the cinnamon-sugar mixture until well coated.