Make the crust: Whisk flour, sugar, and salt. Work cold butter into flour using a pastry cutter or box grater until rough crumbs with pea-sized butter pieces form. Add ice water 1 tablespoon at a time until dough holds when squeezed. Divide into two disks, wrap in plastic, refrigerate at least 45 minutes.
Make the filling: Toss peeled, sliced apples with both sugars, cornstarch, cinnamon, nutmeg, allspice, salt, and lemon juice. Let macerate at room temperature for 20 to 30 minutes, stirring once halfway through.
Preheat oven to 220°C (425°F). Place a baking sheet on the center rack to preheat alongside the oven.
Roll one dough disk to a 32cm circle, 3mm thick. Ease it into the deep-dish pie plate without stretching. Trim overhang to 1.5cm.
Add all the macerating apple slices and their accumulated juice into the lined dish. Arrange into an even mound. Dot with butter pieces.
Roll the second disk to a 32cm circle. Apply as a full top crust with venting slits, or cut into strips and weave a lattice. Seal and crimp the edges.
Brush the entire crust surface with egg wash and sprinkle with sugar. Refrigerate the assembled pie for 15 minutes.
Bake at 220°C (425°F) for 20 minutes, then reduce to 190°C (375°F) without opening the oven. Bake for 35 to 40 more minutes until the crust is deep amber and the filling is actively bubbling with thick bubbles through the vents. Cool completely on a wire rack for at least 2 hours before slicing.