Make the Dough
Place the flour, sugar, and salt into a food processor with the steel blade attachment. Pulse a few times to combine. Add the cold butter and shortening, then pulse 10–12 times until the mixture resembles pea-sized crumbs. Gradually add the ice water while pulsing until the dough just starts to come together—it should be moist but not wet.

Chill the Dough
Transfer the dough onto a floured work surface and bring it together into a ball. Divide into two equal portions, flattening each into a disk. Wrap tightly in plastic wrap and refrigerate for at least 1 hour (or up to 3 days).

Prepare the Filling
Melt the butter in a large, wide-bottomed pan over medium heat. Add the apples and cook for 10 minutes, stirring occasionally, until they become slightly pale. Remove from heat and stir in the cornstarch, cinnamon, nutmeg, allspice, lemon zest, and lemon juice. Gently fold in the blackberries. Let the fruit mixture cool to room temperature, about 20–30 minutes.

Roll Out the Crust
Remove one pastry disk from the refrigerator and place it on a well-floured work surface. Using a floured rolling pin, roll out the dough from the center outward, rotating as you go, until it fits your pie dish. Carefully transfer the dough to the baking dish.

Assemble the Pie
Once the fruit mixture has cooled, spoon it evenly into the pie crust. Roll out the second pastry disk and place it over the filling. Trim any excess dough and crimp the edges to seal. Use a knife to make a few slits in the top crust to allow steam to escape.

Bake the Pie
Preheat the oven to 350°F (175°C). Brush the top crust with beaten egg and generously sprinkle with sugar. Bake for 50–60 minutes, until the crust is golden brown.

Cool and Serve
Let the pie cool for 3–4 hours before slicing and serving. Enjoy!