Step 1: For the Pie Crust: In a large bowl, whisk together the flour, 1 tablespoon granulated sugar, and 1 teaspoon salt.
Step 2: Add the very cold, cubed butter and shortening to the flour mixture. Use a pastry blender, your fingertips, or a food processor to cut the fats into the flour until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining.
Step 3: Gradually add the ice-cold water, 1 tablespoon at a time, mixing lightly with a fork until the dough just comes together. Be careful not to overmix. You may not need all the water.
Step 4: Divide the dough in half, flatten each half into a disc, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes, or up to 2 days.
Step 5: For the Berry Filling: In a very large bowl, gently combine the mixed fresh or mostly frozen berries.
Step 6: In a separate small bowl, whisk together the 1 cup granulated sugar, cornstarch (or flour), lemon zest, and 1/4 teaspoon salt.
Step 7: Sprinkle the sugar-cornstarch mixture over the berries. Gently toss with a rubber spatula until the berries are evenly coated. Be careful not to mash the berries.
Step 8: Dot the berry mixture with the 2 tablespoons of small butter pieces. Set aside.
Step 9: Preheat your oven to 400°F (200°C). Lightly grease a 13×9 inch baking pan.
Step 10: On a lightly floured surface, roll out one disc of dough into a rectangle slightly larger than your baking pan (approximately 15×11 inches). Carefully transfer the dough to the prepared baking pan, gently pressing it into the bottom and up the sides. Trim any excess dough, leaving about a 1/2-inch overhang.
Step 11: Pour the berry filling evenly into the crust-lined pan.
Step 12: Roll out the second disc of dough. You can either place it directly over the filling (and cut several slits for venting), or cut it into strips to create a lattice top.
Step 13: If making a solid top crust, drape it over the filling, trim the edges, and crimp together the top and bottom crusts to seal. If making a lattice, arrange strips of dough over the filling and weave them. Trim and crimp the edges.
Step 14: In a small bowl, whisk the egg with 1 tablespoon of water to create an egg wash. Brush the top crust with the egg wash and sprinkle generously with coarse sugar.
Step 15: Place the slab pie on a baking sheet (to catch any potential drips) and bake for 20 minutes at 400°F (200°C).
Step 16: Reduce the oven temperature to 375°F (190°C) and continue baking for another 40-50 minutes, or until the crust is golden brown and the filling is bubbly and thick. If the crust starts to brown too quickly, loosely tent the pie with aluminum foil.
Step 17: Remove the pie from the oven and let it cool completely on a wire rack for at least 3-4 hours (preferably longer) before slicing and serving. This allows the filling to fully set.