In a saucepan, combine water, butter, sugar, and salt. Bring to a boil over medium heat, stirring until the butter is melted.
Remove from heat and stir in the flour and vanilla until the mixture forms a soft dough.
Allow the dough to cool for about 5 minutes, then add the eggs one at a time, mixing well after each addition until fully incorporated.
Heat oil in a deep frying pan over medium-high heat to 350°F (175°C).
Prepare a piping bag fitted with a star tip, and fill it with the churro dough.
Pipe small bites (about 1-2 inches in length) directly into the hot oil. Fry in batches, avoiding overcrowding, until golden brown (about 2-3 minutes per side).
Remove churro bites using a slotted spoon and drain on paper towels.
In a bowl, mix together the granulated sugar and cinnamon. Roll the churro bites in the sugar mixture while they are still warm until well coated.