In a large bowl, combine the flour and a pinch of salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs.
Gradually add ice water, one tablespoon at a time, mixing until the dough just comes together. Do not overmix. Form into a disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.
Preheat your oven to 375°F (190°C).
In a separate bowl, gently toss the mixed berries with granulated sugar, cornstarch, and lemon juice.
On a lightly floured surface, roll out half of the chilled dough into a 12-inch circle. Carefully transfer it to a 9-inch pie plate. Trim and crimp the edges.
Pour the berry filling into the pie crust.
Roll out the remaining dough for the top crust. You can create a full top crust, cut decorative shapes, or make a lattice. Place the top crust over the filling.
Brush the top crust with the beaten egg wash. If using a full top crust, cut a few vents to allow steam to escape.
Bake for 45-55 minutes, or until the crust is golden brown and the filling is bubbly. If the crust begins to brown too quickly, cover the edges with aluminum foil.
Let the pie cool for at least 2-3 hours before slicing and serving to allow the filling to set.
Notes
This pie is best served slightly warm or at room temperature. It pairs wonderfully with a scoop of vanilla ice cream.