In a large mixing bowl, whisk together flour, powdered sugar, and salt. Cut in vegetable shortening until the mixture resembles coarse meal. Gradually add water and vinegar, mixing until a dough forms. Chill for at least 30 minutes.

Turn the chilled dough onto a lightly floured surface. Roll out half into a 12-inch circle, transfer to a pie plate, and trim excess dough. Refrigerate while preparing the filling.

In a large bowl, combine berries, diced apple, lemon juice, sugar, cornstarch, and a pinch of salt. Toss gently, let sit for 10 minutes while preheating the oven.

Preheat oven to 350°F. Fill the chilled pie crust with the berry mixture, roll out the second half of the dough, and place over the filling. Trim and secure edges, and create slits in the top crust for steam to escape.

Brush the top crust with beaten egg white. Bake for 50-55 minutes until crust is golden brown and filling is bubbly. Cover edges with foil if they darken too quickly.

Carefully remove pie from the oven and let cool on a wire rack for at least 2 hours. Serve warm or chilled, with vanilla ice cream or whipped cream.