In a medium saucepan, combine peeled and sliced fresh peaches with granulated sugar, cornstarch, unsalted butter, and lemon juice. Cook over medium heat for about 5 to 7 minutes until the mixture comes to a gentle boil, stirring frequently to prevent sticking. Once thickened and bubbling, remove from heat and gently fold in the fresh blackberries. Set the filling aside to cool slightly while you prepare the crust.

On a lightly floured surface, roll out one disc of your pie dough until it's approximately 12 inches in diameter. Carefully transfer the dough into a 9-inch pie plate, ensuring it fits snugly against the edges. Trim any excess dough hanging over the rim. Pour the prepared blackberry peach filling evenly into the crust, distributing the fruit evenly across the base.

Roll out the second disc of pie dough to cover the filling. You can choose to cut out decorative shapes for a lattice top or simply place the full sheet over the filling. Seal the edges by crimping them together with a fork or your fingers, and use a sharp knife to cut several slits in the top crust to allow steam to escape. Refrigerate the assembled pie for about 30 minutes to firm up the crust before baking.

While your pie chills, preheat your oven to 400°F (204°C). This high temperature is essential for a perfectly flaky crust.

After chilling, remove the pie from the refrigerator and brush the top crust with the prepared egg wash. If desired, sprinkle coarse sugar over the top. Bake in the preheated oven for 60 to 70 minutes or until the crust is golden brown and the filling is bubbling.

Once baked, remove the pie from the oven and let it cool completely on a wire rack for at least 1 hour before serving. Enjoy your blackberry peach pie warm or chilled!