Boil the liquids. In a medium saucepan, combine water, butter, 2 tablespoons sugar, and salt. Heat over medium until the butter melts and the mixture comes to a gentle boil.
Cook the dough. Remove from heat and add all the flour at once. Stir vigorously with a wooden spoon. Return to low heat and stir for 60–90 seconds, until the dough forms a smooth ball and leaves a thin film on the pan bottom.
Cool 5 minutes. Transfer the dough to a mixing bowl. Let it cool for exactly 5 minutes so the eggs won't scramble.
Add eggs and vanilla. Beat in vanilla, then add eggs one at a time with a hand mixer on medium speed. After each egg, the dough will look broken — keep mixing until glossy and smooth. The final dough should hold a soft V on the beater.
Pipe the churros. Fit a piping bag with a large open star tip. Pipe 4-to-5-inch logs onto a parchment-lined sheet pan, snipping the dough with kitchen scissors. You'll get about 12 churros.
Chill. Refrigerate the piped churros for 30–60 minutes (or freezer 15 minutes) to firm up. Do not chill longer than an hour.
Preheat the air fryer to 375°F (190°C) for 3 minutes. Spray the basket with oil.
Air fry. Arrange churros in the basket with at least 1/2 inch between each — work in batches if needed. Lightly mist with oil. Air fry at 375°F for 10–12 minutes until deep golden brown, flipping halfway if your fryer browns unevenly.
Toss in cinnamon sugar. Mix sugar and cinnamon in a shallow bowl. The moment the churros come out, roll them in the mixture until coated.
Serve immediately with chocolate sauce, dulce de leche, or warm Nutella.