1.Preheat oven to 425 degrees. Line a baking sheet with parchment paper and set aside. In a small bowl, add the egg and water whisk together and set aside.
2.Peel, core, and dice apples into ½" cubes. In a bowl, add apples, brown sugar, cinnamon, and nutmeg. Toss to coat and set aside.
3.On a lightly floured surface, roll out one puff pastry sheet to approximately a 12 inch square. Cut the sheet into four squares.
4.Spoon ¼ cup of apple filling onto half of each square, avoiding ½ an inch around the edges. Fold the opposite corner of each puff pastry over to cover filling. This will form a triangle. Transfer to baking sheet. Repeat with the rest of the squares and continue with the next puff pastry sheet.
5.Press the edges with a fork to seal each pastry. Cut a small vent into the tops of each turnover. Brush the tops of each turnover with egg wash. Sprinkle each turnover with turbinado sugar.
6.Bake for 19-22 minutes, or until turnovers are golden brown. Transfer to a wire rack to cool completely. Serve while still warm.