In a heavy-bottomed pan, bring water, butter, sugar, and salt to a simmer over medium heat.
Reduce heat to low and add flour. Whisk continuously to prevent sticking.
Cook while stirring until the mixture forms a smooth ball, about 8–9 minutes.
Turn off heat and allow the dough to cool for 3–5 minutes.
Add eggs one at a time, whisking well after each addition.
Add vanilla extract and mix until the dough is thick but drops easily. If too stiff, add 1 teaspoon water.
Transfer dough to a double piping bag fitted with a 1M star nozzle.
Heat oil in a heavy pot to 125°C / 257°F.
Pipe churros directly into the oil, cutting into 4-inch lengths.
Fry on medium heat for 4–6 minutes per side until golden brown and fully cooked inside.
Drain on paper towels and immediately coat with cinnamon sugar while hot.