Stir the sugar, cinnamon and salt together in a small bowl. Stir the vanilla into the melted butter.
Unfold the puff pastry on a lightly floured surface and roll it into a 10-inch square.
Brush the pastry with 2 tablespoons of the butter. Sprinkle with three-quarters of the cinnamon sugar and press it in lightly.
Fold the pastry in half into a 10 x 5-inch rectangle. Cut into 10 strips, about 1 inch wide.
Twist each strip 3–4 times and press the ends down. Chill on a plate for 10 minutes.
Preheat the air fryer to 350°F for 3 minutes.
Line the basket with perforated parchment. Add the twists in a single layer with space between them, working in batches.
Air fry at 350°F for 8–10 minutes, flipping halfway, until puffed and deep golden.
Brush the hot twists with the remaining butter and sprinkle with the remaining cinnamon sugar.
For the glaze, whisk the powdered sugar, milk and vanilla until smooth. Cool the twists 2 minutes, then drizzle.