Preheat the Oven:
Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.

Prepare the Cherry Filling:
In a small saucepan, combine the chopped cherries (or cherry pie filling), sugar, cornstarch, and vanilla extract. Cook over medium heat, stirring frequently, until the cherries soften and the mixture thickens (about 5-7 minutes). Remove from heat and let cool slightly.

Prepare the Puff Pastry:
Roll out the puff pastry on a lightly floured surface. Use a sharp knife to cut the pastry into 4 equal squares or rectangles.

Fill the Turnovers:
Spoon a generous tablespoon of the cherry filling into the center of each pastry square. Be careful not to overfill to avoid leakage during baking.

Seal the Turnovers:
Fold each pastry square diagonally to form a triangle. Press the edges together firmly to seal. Use a fork to crimp the edges for extra security.

Egg Wash:
In a small bowl, whisk together the egg and water. Brush the egg wash over the tops of the turnovers to give them a golden finish when baked.

Bake:
Place the turnovers on the prepared baking sheet and bake for 15-20 minutes, or until the puff pastry is golden brown and crisp.

Cool and Serve:
Let the turnovers cool for a few minutes. Optionally, dust with powdered sugar before serving.