In a saucepan, combine water, sugar, salt, and vegetable oil. Bring to a boil.
Remove from heat and stir in flour until a smooth dough forms.
Let the dough cool slightly, then mix in vanilla extract and egg (if using).
Transfer the dough to a piping bag fitted with a star-shaped nozzle.
Heat oil in a deep pan to 180°C (350°F).
Pipe long strips of dough directly into hot oil and cut with scissors.
Fry until golden brown and crispy, about 2–3 minutes per side.
Remove and drain on paper towels.
Roll churros in cinnamon sugar while still warm.
Serve immediately with chocolate or caramel sauce.