Line a baking sheet with parchment paper and set aside. Preheat oven to 400 degrees Peel and chop the apples into small, bite-sized pieces.
In a medium-sized pan, start melting butter and brown sugar over medium heat. Add apples into the brown sugar mixture. Stir occasionally. Sprinkle cinnamon and nutmeg evenly over apples. Stir more until all ingredients are well-combined.
In a small bowl, mix together cornstarch and water. Pour into apple mixture and stir until everything thickens up. Remove pan from heat.
Cut puff pastry into 9 small squares using a. pizza cutter. Place on the lined baking sheet. Scoop a bit of the apple mixture in the center of each puff pastry square. Fold over each puff pastry to form a triangle and press the edges with a fork.
Whisk together egg and milk. Use a pastry brush and brush egg wash over each puff pastry triangle. Sprinkle with sugar.