Preheat oven to 400℉. Cover two cookie sheets with parchment paper. Set aside.
In a bowl, combine apples, brown sugar, cinnamon, nutmeg, salt and cheddar cheese. Set aside.
In a small bowl, mix together beaten egg and water to make the egg wash. Set aside.
Cut each sheet of puff pastry into 4 rectangles. Brush edges with egg wash. Place approximately 2 tablespoons of the apple mixture in the center of each rectangle. Fold over diagonally and press firmly with a fork to seal the edges.
Place on cookie sheet and brush top with egg wash. Cut two small slits into each turnover to vent. Sprinkle with raw sugar, if desired.
Bake for 20 minutes or until turnovers are golden. Best served warm.