Preheat the oven to 200C/400F. Take the puff pastry out of the fridge at least 30 minutes before working with it.
Peel the apples, core them and slice them quite thinly and then cut the slices into smaller chunks. In a saucepan combine the apples, brown sugar, butter, cinnamon, nutmeg and corn starch. Cook over low heat while stirring to avoid burning for 10-15 minutes until apples are tender but not falling apart, and the juices from the apples are thick from corn starch. A spoon should leave a trail on the bottom of the pan when stirring. Take the apples off the heat and cool completely.
In a small bowl mix the caster sugar and cinnamon. Set aside.
Unroll your puff pastry sheet and cut into 12 squares. Put about 2 tbsp of the apple filling on one corner of a pastry square. Avoid getting too much liquid on your pastry. Then take the opposite corner of the square and fold over to form a triangle. Pinch the sides and then crimp with a fork. Repeat until all pastry squares are filled. Repeat with another sheet of puff pastry.
Arrange apple turnovers on a parchment paper lined, rimmed baking sheet. Brush with a beaten egg all over, and especially the seams. Then sprinkle with cinnamon sugar and slash each pastry with a sharp knife twice. Bake in the preheated oven for 25 minutes or until golden and puffed up. You might need to bake all apple turnovers in batches depending on the size of your oven.