Preheat oven to 450 degrees F (230 degrees C). Line a baking sheet with parchment paper.
Roll each pastry out onto a lightly flour work surface and cut each into quarters.
Spread about 2 tablespoons mashed potatoes onto 4 of the pastry quarters, spreading to within 1/3-inch of the edges. Top mashed potatoes with 2 tablespoons turkey and 1 tablespoon cranberry sauce.
Whisk egg and water together in a bowl. Brush egg mixture onto outside edges of prepared pastry quarters. Top each prepared quarter with remaining pastry quarters; press and crimp edges with a fork to seal. Cut a slit in the top of each pastry wedge and brush each with egg mixture. Transfer wedge pies to prepared baking sheet.
Bake in the preheated oven until golden brown, 15 to 20 minutes.