In a mixing bowl, combine the all-purpose flour, granulated sugar, and salt. Cut in the chilled, diced unsalted butter until the mixture resembles coarse crumbs. Gradually add ice-cold water, mixing until the dough forms. Divide it in half, shape into discs, wrap in plastic, and chill for at least 2 hours.

In a large bowl, gently combine halved strawberries, blackberries, lemon juice, and granulated sugar. Allow the mixture to sit for about 10-15 minutes to release juices. Using a slotted spoon, drain excess liquid.

Roll out one dough disc on a lightly floured surface to about 1/8 inch thick. Transfer to a rimmed baking sheet lined with parchment paper. Spoon the berry filling evenly over the crust. Roll out the second crust, place it over the filling, and cut slits for steam to escape.

Preheat your oven to 375°F (190°C). Brush the top crust with an egg wash for a golden finish. Bake for approximately 50 minutes or until the crust is a rich, golden brown.

Allow the pie to cool completely on a wire rack before slicing into squares and serving.