In a medium saucepan over medium heat, melt the butter and add in apples. Cook for 5 minutes until they are just starting to soften.
Drop the heat to low and add in brown sugar, white sugar, cornstarch, cinnamon, and salt. Cook for 3-5 more minutes until apples are soft but not mushy. Remove from heat and allow to cool completely before using.
On a lightly floured surface, use a rolling pin to roll each puff pastry sheet into an 11-inch square. With a pizza cutter, cut each sheet of puff pastry into 4 equal squares. If at any point the pastry is getting soft, place in the fridge for 10 minutes.
Place 1-2 tablespoons of the apple filling in the center of one square, pay attention to not get any on the edges.
In a small bowl, beat together the egg with 1 tablespoon of milk. Brush the egg wash on two of the sides (just enough to seal it).
Fold one corner over the filling to another corner to form a triangle. Press down on edges to seal together then crimp with a fork. Repeat with remaining pastries.
Cut 2-3 small slits with a sharp knife in the top of each one. Brush egg wash all over the top.
Preheat the oven to 375°F and place the pastries not touching in the refrigerator for 15 minutes.
Line two 13x9-inch baking sheets with parchment paper. Place the assembled turnovers about 1-inch apart on prepared baking sheets.
Bake for 20-25 minutes until golden brown.
In a small bowl, mix together the powdered sugar and milk. Drizzle glaze over the warm pastries.