Combine the apples, cornstarch, vanilla extract, cinnamon, and brown sugar in a pan and heat over medium for 5 minutes, stirring constantly. Reduce to low and simmer for 5 minutes. Remove from heat and let cool.

Lay out the puff pastry sheets. Cut each sheet into 4 squares, for 8 squares total.

Spoon a few tablespoons of apple filling into the center of each square. Fold one corner of the square over the filling to make a triangle. Crimp the edges with a fork to seal. Place the turnovers on a plate or dish and refrigerate for at least 15 minutes (up to 1 hour / or freeze to bake later).

Preheat the oven to 400°F (200°C). Line a large baking sheet with parchment paper.

Transfer the turnovers to the baking sheet. Whisk together the egg and milk, then brush the mixture over the tops. Cut a few slits in the top of each to vent steam. Bake for 25 minutes, until golden brown. If the turnovers are browning unevenly, rotate the baking sheet.

Let the turnovers cool for a few minutes before serving, with caramel sauce, if desired.