How to Make It
Stir together water, butter, salt, and 2 tablespoons of the sugar in a large saucepan over medium-high; cook, stirring occasionally, and bring to a boil. Turn off heat, and immediately add flour all at once and stir until well combined.
Transfer dough to a stand mixer fitted with a paddle attachment. Beat on low speed to cool mixture slightly, about 2 minutes. Add eggs, 1 at a time, beating on medium-low until each egg is incorporated. Beat in vanilla. Increase speed to medium, and beat until mixture is cooled to room temperature, about 8 minutes.
Chill dough 10 minutes. Place dough in piping bag fitted with a wide star tip.
Preheat air fryer to 400°F. Spray air fryer basket with cooking spray. Pipe dough into 4-inch strips directly onto fryer basket, and cut end with kitchen shears. Lightly coat tops with cooking spray. Close lid, and cook until golden and slightly crisp, 6 to 8 minutes, flipping half way through; set aside. Repeat process with remaining dough in batches.
Stir together cinnamon and remaining 3/4 cup sugar in a shallow dish. Brush each churro with melted butter, and dredge in cinnamon sugar. Serve immediately with chocolate sauce or dulce de leche, if desired.