Preheat oven to 400°.
Mix diced apples with brown sugar and cinnamon in a bowl
Melt butter in a large skillet over medium heat.
Add apples and cook, stirring often about 5 minutes or until apples are softened.
Place in a bowl and cool completely. Pop the bowl in the freezer for about 10 minutes to speed up the cooling process.
Remove one sheet of puff pastry from the refrigerator, leaving one sheet in the refrigerator to stay chilled. Lightly flour a clean surface and place the puff pastry over the flour. Dust the top lightly with a bit more flour.
Using a rolling pin, roll the puff pastry into about a 10 x 12 inch rectangle.
Cut the puff pastry into 4 squares using a pizza wheel.
Beat egg and water together in a small bowl.
Spoon apple pie filling into the center of each square.
Brush the edges of each puff pastry square with egg wash.
Fold puff pastry over apple filling into a triangle. Use a fork to crimp the edges to seal.
Place turnovers onto a parchment paper lined baking sheet, spacing about 3 inches apart.
Use a sharp knife to cut a couple of small slits in the top of each pastry.
Brush all over with egg wash.
Bake for 20 minutes or until golden brown.
Remove from oven to a wire rack and cool slightly.
Repeat with remaining ingredients.
Mix powdered sugar with milk and vanilla extract in a small bowl with a whisk until smooth.
Drizzle over apple turnovers.
Serve warm or at room temperature.