Cook the apples, cranberries, brown sugar, cinnamon, nutmeg, lemon juice, and vanilla in a large skillet over medium heat for 6 to 8 minutes, stirring occasionally, until the apples begin to soften and the cranberries start to burst.

Stir together the cornstarch and water, then add the mixture to the fruit. Cook for 1 minute more, stirring constantly, until the filling thickens. Transfer the filling to a bowl and let it cool completely.

Preheat the air fryer to 350°F for 3 to 5 minutes.

Whisk together the egg and 1 tablespoon of water to make an egg wash.

Unfold the puff pastry sheets and cut each sheet into four equal squares.

Spoon about 2 tablespoons of the cooled filling into the center of each pastry square.

Brush the edges with the egg wash, fold the pastry diagonally into triangles, and press the edges together with a fork to seal.

Cut two or three small slits in the top of each turnover, then brush the tops with the remaining egg wash and sprinkle with coarse sanding sugar, if using.

Lightly spray the air fryer basket with nonstick cooking spray and arrange the turnovers in a single layer, leaving space between them. Cook in batches if needed.

Air fry for 10 to 12 minutes, or until the turnovers are puffed, crisp, and deep golden brown.

Let the turnovers cool for about 10 minutes.

Whisk together the powdered sugar, milk, and vanilla until smooth, then drizzle over the warm turnovers.