Combine water, butter, sugar, and salt in a saucepan, bring to a boil, then stir in flour and vanilla and cook until a smooth dough forms, about 1 minute.

Let dough cool slightly, then beat in eggs one at a time until glossy and thick. Transfer to a piping bag with a large star tip and pipe 4‑inch lengths onto a parchment lined tray. Chill 10 minutes if the dough is soft.

Heat 2 inches of oil to 350°F (175°C) and fry churros in batches for 3 to 4 minutes, turning once, until deep golden. Drain on paper towels.

Toss warm churros in the cinnamon sugar mixture and serve immediately.