Break your chilled pie dough into two pieces that are roughly the same size.
Transfer to a lightly floured surface and roll one piece into a rectangle about ⅛" thick.
Using a pizza cutter (or a knife and a straight-edge, such as a clean ruler), neatly cut dough int 4.5" squares and transfer to a parchment-paper-lined baking sheet (you will need to gather the scraps and re-roll them out to make all 10 turnovers).
Place squares on a parchment paper lined cookie sheet and return to the refrigerator.
Repeat rolling and cutting with your second half of pie dough.
Prepare your apple filling by combining your apples, brown sugar, and butter in a medium-sized saucepan over medium-low heat.
Stir frequently until butter is melted, then add cornstarch, cinnamon, vanilla extract, and salt.
Increase heat to medium and bring to a simmer and simmer for 5 minutes, stirring occasionally.
Remove from heat and allow mixture to cool (at least 15-20 minutes) before proceeding.
Prepare egg wash by combining egg and teaspoon of water in a small dish and stir/scramble well.
Lightly brush the insides of your pastry squares with egg wash.
Portion about 2-3 Tablespoons of apple pie filling into the center of each square. Gently fold over one corner to the other to envelope the apple filling. Use the tines of a fork to press and seal the turnovers.
Brush the outside lightly with egg wash, cut small slits across to vent, and sprinkle with coarse sugar, if desired.
Bake on 400F (205C) oven for 25 minutes, until pastry is beginning to turn golden brown.
Allow to cool before drizzling with glaze.
Whisk together powdered sugar, 2 teaspoons of milk, and vanilla extract in a small bowl. If mixture is too stiff to drizzle, add more milk, another teaspoon at a time, until a fluid consistency is reached.
Drizzle over slightly cooled turnovers. Enjoy while still warm or allow glaze to harden before enjoying.