Position the oven racks in the upper and lower thirds of the oven; preheat to 375 degrees. In a large skillet, cook the berries and brown sugar over medium-high, stirring often, until juices form, 2 to 3 minutes. Add the cornstarch, lemon zest, juice, cinnamon and a small pinch salt. Cook, stirring often, until the juices thicken, about 4 minutes. Spread the filling on a rimmed baking sheet. Refrigerate until cold, about 30 minutes.
On a lightly floured surface, roll out each piecrust to a 13-inch round. Cut each into 8 wedges, like a pizza, and place 4 wedges each on 2 parchment-lined baking sheets. Spoon a scant 1/4 cup filling onto each of the wedges, mounding in the center and leaving a 1/2-inch border on the sides and a 1 1/2-inch border at the wide end. Brush the borders lightly with the beaten egg. Cover with the remaining 8 wedges, pressing the side edges firmly to seal. At the wide end of each wedge, fold the crust over; crimp decoratively. Brush with more egg; dust generously with confectioners' sugar. Cut 2 slits on top of each turnover.
Bake the turnovers, switching the sheets halfway through, until the crust is deep golden brown and the filling is bubbling through the slits, 35 to 45 minutes. Let cool 10 minutes. Transfer the turnovers, on the parchment, to racks. Run a thin knife around the edges to release them from any juices stuck to the parchment. Dust with more confectioner's sugar. Serve at room temperature.