Preheat oven to 400°F. Line two baking sheets with parchment paper.

If using store-bought puff pastry, unfold the thawed sheets on a lightly floured surface. If using homemade rough puff pastry, roll the chilled dough on a lightly floured surface into two 10-inch squares, about ⅛ inch thick. Cut each sheet into 4 equal squares, giving you a total of 8 squares.

Place 1-2 tablespoons of peach pie filling in the center of each square.

In a small bowl, beat the egg with 1 tablespoon of water to make an egg wash. Brush the edges of each square with egg wash.

Fold each square diagonally to form a triangle. Press edges firmly to seal. Use a fork to crimp the edges closed.

Transfer the turnovers to the prepared baking sheets. Place the baking sheets in the freezer for 10 minutes to chill the pastry.

Remove from the freezer, brush the tops with the remaining egg wash, and sprinkle with coarse sugar (optional).

Bake for 18-20 minutes, until puffed and golden brown.

Allow to cool on the baking sheet for 5 minutes, then transfer to a wire rack.

Dust with powdered sugar just before serving, or whisk together the powdered sugar, milk, and vanilla to make the optional glaze. Drizzle the glaze over the cooled turnovers and let it set before serving.