In a bowl, mix together the flour, salt, and powdered sugar. Cut in the vegetable shortening until the mixture resembles coarse crumbs. Gradually sprinkle in cold water and cider vinegar, mixing until the dough holds together. Divide into halves, shape into disks, wrap in plastic, and refrigerate for at least 1 hour.

In a large mixing bowl, combine mixed berries and diced apple. Drizzle with lemon juice, then sprinkle with sugar, cornstarch, and salt. Gently toss to coat and allow juices to meld.

On a lightly floured surface, roll out one disk of dough to fit a 9-inch pie plate, about a 12-inch circle that's ¼-inch thick. Transfer into the pie plate, pressing into the bottom and sides. Prick the bottom to prevent bubbling and add the berry filling.

Roll out the second disk for the top crust. Place over the filling, trim excess dough, and crimp the edges. Cut slits in the crust to allow steam to escape.

Whisk together egg white with a teaspoon of water. Brush over the top crust for a glossy finish.

Preheat oven to 350°F (175°C). Place pie on a baking sheet and bake for 50-55 minutes, or until golden brown. Shield edges with foil if browned too quickly.

Remove from oven and let cool on a wire rack for at least 2 hours to set the filling.