Peel, core, and dice the apples into small cubes (about 1/2-inch).
Add apples to a skillet over medium heat. Stir in sugar, cinnamon, and a pinch of salt. Cook, stirring often, until apples soften and release juices.
Sprinkle in cornstarch and stir well. Cook until the liquid looks glossy and slightly thick. Remove from heat and cool to room temperature.
Preheat oven to 400°F (200°C) (assumption). Line a baking sheet with parchment. Cut puff pastry into squares. Add filling to one side, fold into triangles, seal edges, and crimp with a fork. Chill assembled turnovers in the refrigerator for 15–20 minutes .
Brush the chilled turnovers with whisked egg.
Bake until puffed and deep golden brown.
Cool 10 minutes, then dust with powdered sugar and serve.