Make the pie crust: In a large bowl, whisk together flour, salt, and sugar. Cut in cold butter using a pastry blender or fingertips until mixture resembles coarse crumbs. Gradually add ice water, 1 tablespoon at a time, mixing until dough just holds together. Divide dough in half, flatten into discs, wrap in plastic, and refrigerate for at least 1 hour.
Preheat oven to 400°F (200°C).
In a large bowl, combine cherries, mixed berries, sugar, cornstarch, lemon juice, and vanilla. Toss gently to coat.
On a lightly floured surface, roll out one disc of dough to a 12-inch circle. Transfer to a 9-inch pie dish, letting excess hang over edge. Pour in the filling and dot with butter pieces.
Roll out the second disc of dough to a 12-inch circle. Place over filling. Trim excess dough, leaving a 1-inch overhang. Fold edges under and crimp as desired. Cut several slits in top crust to vent steam.
Brush top crust with beaten egg and sprinkle with coarse sugar.
Place pie on a baking sheet. Bake for 20 minutes, then reduce oven temperature to 375°F (190°C) and bake for 30-35 minutes more, until crust is golden and filling is bubbly. If edges brown too quickly, cover with foil.
Cool on a wire rack for at least 2 hours before slicing to allow filling to set.
Tips
Serve warm with vanilla ice cream or whipped cream.
Store leftovers covered at room temperature for up to 2 days.
For a lattice top, cut the second dough into strips and weave over filling.