1. Preheat the oven to 400°F (200°C) or according to your puff pastry package directions. Line a baking sheet with parchment paper.

2. Lightly flour your work surface and unfold the thawed puff pastry sheets. Gently roll them to even out the thickness, then cut each sheet into about 4 equal squares for a total of 8 squares.

3. In a medium bowl, beat the softened cream cheese, 1/3 cup granulated sugar, 1 teaspoon vanilla extract, and lemon zest until smooth and creamy.

4. In a separate bowl, combine the chopped strawberries, 2 tablespoons granulated sugar, and cornstarch. Toss until the strawberries are evenly coated.

5. Place a puff pastry square in front of you like a diamond. Spoon a tablespoon or so of cheesecake filling into the center, then top with a spoonful of the strawberry mixture, leaving plenty of border around the edges.

6. In a small bowl, whisk the egg and water together to make an egg wash. Brush the edges of the pastry square with the egg wash.

7. Fold the pastry over to form a triangle, pressing the edges firmly to seal. Crimp the edges with a fork to help keep the filling inside. Repeat with the remaining pastry squares and fillings.

8. Transfer the turnovers to the prepared baking sheet, leaving space between each one. Brush the tops with more egg wash.

9. Use a sharp knife to cut a small slit or two on top of each turnover to let steam escape.

10. Bake for 16 to 20 minutes, or until the turnovers are puffed and deep golden brown with no raw dough remaining.

11. Let the turnovers cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool slightly.

12. While the turnovers cool, whisk together the powdered sugar, 1 tablespoon milk or cream, and 1/2 teaspoon vanilla extract until smooth. Add a few more drops of milk if needed until the glaze is thick but pourable.

13. Drizzle the vanilla glaze over the warm turnovers. Allow the glaze to set for a few minutes, then serve and enjoy.