1. Preheat the oven to 400°F and line a baking sheet with parchment paper.

2. Add the chopped strawberries, granulated sugar, cornstarch, and lemon juice to a small saucepan.

3. Cook over medium heat, stirring often, until the strawberries soften and the filling thickens, about 5 to 7 minutes.

4. Remove from the heat, stir in the vanilla extract, and let the filling cool completely.

5. In a small bowl, mix the softened cream cheese and powdered sugar until smooth.

6. Roll out the puff pastry lightly and cut it into 4 equal rectangles.

7. Place the rectangles on the prepared baking sheet.

8. Spread some cream cheese mixture in the center of half the rectangles, leaving a border around the edges.

9. Spoon the cooled strawberry filling over the cream cheese layer.

10. Top with the remaining pastry rectangles or fold the pastry over, then seal the edges gently with a fork.

11. Whisk the egg with the water and brush the tops of the pastries.

12. Bake for 15 to 18 minutes, or until puffed and golden brown.

13. Cool slightly, then dust with powdered sugar before serving.