In a small bowl, whisk together the egg and water. Set aside.
Place the puff pastry on a lightly floured surface and roll to 1/8-inch thick. Cut 12 (3 3/4- inch) circles from the puff pastry. If the dough begins to stick, lightly dust with flour.
Place 2 teaspoons of the fruit compote onto the middle of each circle. Lightly brush the edges with the egg wash and fold the pastry over so that the edges meet. Using a fork, press the edges together to seal. Brush the tops of the pies with the egg wash and poke several holes in the top of the pies for steam to escape.
Place the pies 1-inch apart on a baking sheet lined with parchment paper and bake until golden brown, approximately 25 minutes.