Preheat oven to 400°F (200°C).
Line a baking sheet with parchment paper.
In a medium bowl, combine the diced apples, cornstarch, vanilla extract, cinnamon, and sugar. Toss to coat evenly.
Unfold the puff pastry sheets on a lightly floured surface. Cut each sheet in half to create four equal rectangles.
Spoon about 1/4 cup of the apple mixture onto one half of each pastry rectangle, leaving a 1/2-inch border.
Brush the edges of the pastry with water.
Fold the other half of the pastry over the filling to create a turnover shape. Press the edges firmly with a fork to seal.
Cut a few small slits in the top of each turnover to allow steam to escape.
Place the turnovers on the prepared baking sheet.
Whisk the egg with 1 tablespoon of water to make an egg wash. Brush the tops of the turnovers with the egg wash.
Bake for 20-25 minutes, or until the pastry is golden brown and puffed.
Let the turnovers cool slightly on the baking sheet before transferring them to a wire rack.
Drizzle with caramel sauce, if desired, once slightly cooled.