The sweetness of strawberries & raspberries makes a perfect filling for this lattice-topped pie. The bright red color of berries peeks through the topping just enough to see the fruit juices bubbling and thickening as it bakes.
Place flour and salt in bowl of a food processor and pulse until combined. Add butter and shortening and pulse until mixture resembles coarse crumbs. Add water, one tablespoon at a time and pulse just until dough comes together (be careful to not over mix). Pat dough into 2 disks (one slightly larger than the other) and wrap in plastic wrap. Chill at least 30 minutes.
Roll out larger disk of dough on a lightly floured surface to a 12-inch circle. Gently transfer dough to 9 1/2-inch pie plate. Leave edges untrimmed and set aside in the refrigerator.
Hull strawberries and cut in quarters if large or cut in half if smaller. Place strawberries, raspberries, sugar, cornstarch and brandy in a large bowl and stir until combined. Set aside. Berries are best if prepared just prior to completing pie.
Preheat oven to 400°F. Roll out smaller disk of dough into an 11-inch circle. With a pastry cutter or knife, cut dough into 12 strips (about 3/4-inch-wide each). Remove pie shell from refrigerator. Fill with berry mixture and dot with butter pieces.
Lay 6 dough strips across filling. Fold back every other strip slightly more than halfway. Place one strip perpendicular to the others and unfold strips back down. Fold back alternate strips and place another strip over filling. Unfold strips and repeat with remaining pastry strips until you have weaved a lattice pattern. Trim ends of strips and fold over with overhang of dough from pie shell. Crimp to form decorative pattern. Brush crust with beaten egg yolk.
Place a sheet of aluminum foil under pie to catch any drippings. Bake 45 to 50 minutes or until bubbling and golden. Let cool on a wire rack at least 2 hours.