Melt the butter in a small skillet over medium heat. Add the diced apples, sugar, cinnamon, cornstarch, and lemon juice. Cook for about 5 minutes, stirring, until the apples soften and the liquid thickens. Cool the filling completely.

Roll the puff pastry into a 12-inch square and cut into 4 equal squares. Place a heaping tablespoon of cooled filling in the centre of each, brush the edges with egg wash, fold into triangles, and press the edges with a fork to seal. Brush the tops with egg wash and sprinkle with coarse sugar if using.

Preheat the air fryer to 375°F (190°C). Place the pies in the basket in a single layer and air fry for 10 to 12 minutes, until deeply golden. Cool 5 minutes on a wire rack, dust with powdered sugar, and serve warm.