Mixed Berry Hand Pies

Whisk all-purpose flour, whole-wheat flour, 1 tablespoon sugar and salt in a medium bowl. Cut butter into the flour using a pastry blender or your fingertips, leaving some pea-sized chunks remaining. Add just enough water to moisten, tossing with a fork to combine. The mixture will become shaggy and start to come together. (Note: There will be 2 to 3 tablespoons dry mixture in the bottom of the bowl.) Empty the shaggy dough onto a large piece of plastic wrap. Use the wrap to press the dough into a disk. Refrigerate for at least 20 minutes. Divide the dough into 10 pieces and form each one into a disk.

Arrange two oven racks evenly in upper and lower thirds of oven. Preheat oven to 350 degrees F. Line two large rimmed baking sheets with parchment paper.

Lightly dust work surface with flour. Roll each dough disk into a 6-inch round, about 1/8 inch thick. Transfer the dough rounds to the prepared baking sheets, spacing evenly.

Stir raspberries, blueberries, cornstarch and 1/3 cup sugar together in a medium bowl. Using about 2 tablespoons berry mixture for each dough round, divide the berry mixture among the dough rounds, placing it on half of each round and leaving a 1-inch border around the edges. Do not overfill. Brush egg mixture along the edge of half of the circle. Fold the dough in half to cover the berry mixture. Crimp edges with a fork to seal.

Brush the egg mixture over the crusts. Sprinkle the pies with the remaining 1 tablespoon sugar. Cut three small vent holes in each pie. Bake, switching the positions of the baking sheets halfway through baking, until the crusts are golden and the filling is bubbling, 25 to 35 minutes.