Place a rimmed baking sheet on the center rack and preheat the oven to 425F.
Fit one crust into a 9-inch ceramic pie dish and refrigerate while preparing the filling.
In a large bowl, combine the frozen berries, both sugars, cornstarch, and salt. Add the vanilla extract, almond extract, and grated apple. Toss until evenly coated.
Pour the filling into the chilled crust. Dot the top evenly with the butter pieces.
Cut the second crust into strips and arrange in a lattice pattern over the filling. Trim and crimp the edges.
Brush the lattice and edges thoroughly with the egg wash. Sprinkle with turbinado sugar.
Refrigerate the assembled pie for 15-20 minutes.
Place the pie on the preheated baking sheet. Bake at 425F for 20 minutes.
Reduce heat to 375F and bake for an additional 40-55 minutes, until the crust is deep golden brown and the filling is actively bubbling in the center. Tent the edges with foil if browning too quickly.
Transfer to a cooling rack and cool for at least 4 hours before slicing. Do not cut while warm.