Preheat the oven to 375°F (190°C). Line a 13x18-inch baking sheet with parchment paper.

In a large bowl, whisk together the flour, salt, and sugar. Add the chilled butter and mix until the mixture resembles coarse crumbs.

Gradually add ice water, one tablespoon at a time, mixing until the dough comes together. Divide the dough in half, flatten into disks, wrap in plastic wrap, and chill in the refrigerator for at least 30 minutes.

In another bowl, combine the mixed berries, granulated sugar, cornstarch, vanilla extract, and lemon juice. Gently toss to coat the berries evenly.

Roll out one disk of dough on a floured surface to fit the baking sheet. Place the rolled dough onto the prepared baking sheet.

Pour the berry mixture onto the dough, spreading it evenly.

Roll out the second disk of dough and place it over the berry filling. Trim any excess dough and crimp the edges to seal. Cut slits in the top crust to allow steam to escape.

Brush the top crust with the beaten egg and sprinkle with coarse sugar.

Bake for 45-50 minutes, or until the crust is golden brown and the filling is bubbly.

Allow the pie to cool for at least 1 hour before slicing.