For the crust:
1 large egg beaten with 1 tbsp. water
To make the pie crust, combine the flours, sugar, and salt in a medium bowl. Stir with a fork to blend. Add in the butter and toss gently to coat. Cut the butter into the dry ingredients using a pastry blender or two knives until the mixture is coarse and the largest butter pieces are no bigger than peas. Stir in the water until the dough comes together. Mix very gently so that it forms a cohesive ball, being careful not to overwork the dough. Form into a disc, wrap tightly with plastic wrap and refrigerate until firm, 1-2 hours.
To assemble the pies, line a baking sheet with a silicone baking sheet or parchment paper. Place the dough on a lightly floured work surface. Roll out in a thin even layer, a bit less than ¼-inch thick. Using a smaller round biscuit or cookie cutter (approximately 2¼-inch diameter) to cut out 8 rounds of dough. Transfer these to the prepared baking sheet. Use a slightly larger cutter (approximately 2¾-inch diameter) to cut out 8 more rounds, rerolling dough scraps as needed. Use a small paring knife to make small slits in each of these to vent steam during baking. Sprinkle a little bit of the chopped chocolate in the center of each dough round on the baking sheet, leaving a clear rim at the edge to seal the pies. In a medium bowl, combine the berries, sugar, cornstarch and lemon juice, folding together until evenly mixed. Place a few of the berries on top of the chocolate on each round, and top each with one of the larger dough rounds. Gently pinch together the edges of the dough rounds and use the tines of a fork to crimp together. Transfer the baking sheet to the freezer and chill the assembled pies for 30 minutes.
Preheat the oven to 375˚ F. Lightly brush the tops of the pies with the egg wash. Bake, rotating halfway through the bake time, until lightly browned and juices begin to bubble through the vents, about 25-27 minutes total. Transfer to a wire rack and let cool slightly before serving.