Prepare the Apple Filling: In a medium saucepan, combine diced apples, water, sugar, cornstarch, lemon juice, and cinnamon. Cook over medium heat, stirring frequently, until the mixture thickens and the apples soften, about 10–12 minutes. Remove from heat and let it cool completely.

Prepare the Cream Cheese Filling: In a medium bowl, beat cream cheese, sugar, egg yolk, lemon juice, and vanilla extract until smooth and creamy. Set aside.

Prepare the Puff Pastry: Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper. Roll out the puff pastry sheets on a floured surface and cut them into squares or rectangles.

Assemble the Pastries: Place a spoonful of cream cheese filling in the center of each puff pastry square, then top with a spoonful of the cooled apple filling. Fold or shape the pastry as desired (e.g., sealing the edges or creating turnovers).

Apply Egg Wash: In a small bowl, whisk together the egg and water. Brush the tops of the pastries with the egg wash and sprinkle with coarse sugar for a golden, sweet crust.

Bake: Place the assembled pastries on the prepared baking sheet and bake for 18–22 minutes or until golden brown and puffed. Allow to cool slightly before serving.