Add the brown sugar, cinnamon, and nutmeg and cook an additional 3 minutes, stirring until the apples are coated and the sugar melts. Remove from heat.
Cut one thawed puff pastry sheet into four squares.
Add a heaping spoonful of the apple mix to each square, then fold the square over to create a triangle.
Press the edges shut to seal. Use a fork to pinch the edges further.
Cut a small hole into the top of the turnover to allow the turnover to breathe while cooking.
Repeat with the second puff pastry sheet.
Place turnovers on a greased baking sheet.
Cook at 400 degrees for 25 minutes.
Mix powdered sugar, milk, and vanilla together in a bowl.
Allow the turnovers to cool completely.
Drizzle mix generously over the cooled turnovers.
*Keep puff pastry sheets cool until ready to use. **Try to seal each turnover as well as possible to prevent the apple mix from leaking out. ***If your pastries puff too much, simply press them down lightly after they come out of the oven.