Heat the water, butter, 1 tbsp sugar and salt in a medium saucepan over medium heat until the butter melts and it comes to a full boil.

Add the flour all at once and stir hard. Keep stirring over low heat for 1 to 2 minutes, until the dough forms a ball and leaves a thin film on the pan.

Transfer to a bowl and cool for 5 minutes.

Beat in the eggs one at a time, then the vanilla. The dough should be thick and glossy and hold a peak that slowly folds over.

Spoon into a piping bag fitted with a large open-star tip (Wilton 1M). Pipe 6-inch churros onto strips of parchment, rotating the bag about half a turn as you pipe for twisted ridges.

Mix the 1/2 cup sugar and cinnamon in a shallow dish.

Heat 2 inches of oil to 375F (190C), using a thermometer.

Lower 3 or 4 churros into the oil on their parchment strips. Remove the paper with tongs once it releases, after about 20 seconds.

Fry 2 to 3 minutes per side until deep golden. Drain on a wire rack for 30 seconds, then roll in cinnamon sugar while hot. Let the oil return to 375F between batches.

Freeze the piped churros on their parchment for 20 minutes so they hold their ridges.

Spray all sides with oil. Air fry at 380F (193C) for 8 to 10 minutes in a single layer, flipping and spraying again at 5 minutes.

Roll in cinnamon sugar right away, spraying once more if it will not stick.