Whisk together the flour, 1 tbsp granulated sugar, and ½ tsp salt. Work in the cold butter and shortening until the mixture resembles rough breadcrumbs. Add ice water 1 tbsp at a time until the dough just holds together, press into 2 disks, wrap, and refrigerate for at least 1 hour.

Toss the sliced apples with the 150g granulated sugar, 50g brown sugar, 3 tbsp cornstarch, 1½ tsp cinnamon, ¼ tsp nutmeg, ¼ tsp allspice, ¼ tsp salt, and 1 tbsp lemon juice. Let sit for 15 minutes, then drain the excess liquid.

Preheat the oven to 220°C (425°F). Roll 1 dough disk into a 33cm (13-inch) circle and line a 23cm (9-inch) deep-dish pie dish, leaving a 2cm overhang.

Spoon the apple filling into the crust, mounding it 4 to 5cm above the rim. Scatter the 2 tbsp cubed butter over the filling, top with the second rolled crust, press and crimp the edges, cut 5 or 6 vents, brush with the egg wash, and sprinkle with the 1 tbsp coarse sugar.

Bake at 220°C (425°F) for 20 minutes, then reduce to 175°C (350°F) and bake for 45 to 50 minutes until deep amber and bubbling. Cool on a wire rack for at least 2 hours, then serve warm with the filling visible through the golden vents.