Preheat the oven according to the package directions for the puff pastry. Line two baking sheets with parchment paper and set aside.
In a large bowl, combine the chopped apples, granulated sugar, flour, apple pie spice, salt, apple cider vinegar, and lemon juice. Stir until the apples are evenly coated.
Let the apple mixture rest for 30 minutes to allow the fruit to release some of its juices.
Unfold the puff pastry sheets on a lightly floured surface. Cut each sheet into approximately 4-inch squares using a pizza cutter or sharp knife.
Place about 1 tablespoon of the apple filling in the center of each pastry square.
Fold each square diagonally to form a triangle. Press the edges together firmly to seal.
Crimp the edges with a fork and cut two small slits in the top of each turnover to allow steam to escape.
Arrange the turnovers on the prepared baking sheets, leaving space between each one.
Bake for 12 minutes, or until the pastry is puffed and golden brown.
Transfer the turnovers to a wire rack and allow them to cool slightly.
Meanwhile, whisk together the powdered sugar, apple pie spice, maple syrup, and enough milk to create a smooth drizzle.
Drizzle the icing over the warm turnovers and allow it to set before serving.
Notes
Letting the apples sit for 30 minutes helps draw out moisture and creates a more flavorful filling.
Make sure the oven is fully preheated before baking. Puff pastry needs a hot oven to rise properly.
Avoid opening the oven during the first 10 minutes of baking or the pastry may not puff as well.
Transfer the turnovers to a wire rack after baking to help keep the bottoms crisp.
Store leftovers in an airtight container at room temperature for up to 1 day or in the refrigerator for up to 3 days.
Reheat in a 350 degree F oven for 5 to 7 minutes to restore the flaky texture.
Unbaked turnovers can be assembled and refrigerated for up to 24 hours before baking.