Step 1

Mix salt and 2¾ cups flour in the bowl of a stand mixer fitted with paddle attachment on low speed to combine. Add butter and shortening and beat on medium-low until mixture resembles coarse cornmeal. Drizzle in ⅓ cup ice water, then beat, adding splashes of ice water as needed, until dough just comes together. Turn out onto a lightly floured surface. Gently press together and flatten a couple of times, about 30 seconds. Divide dough in half; pat into disks. Wrap in plastic; chill at least 2 hours.

Step 2

Do Ahead: Dough can be made 3 days ahead. Keep chilled.

Step 3

Preheat oven to 350°. Toss apples, 1 cup granulated sugar, and ¼ cup flour in a large bowl. Divide between 2 rimmed baking sheets; bake, rotating baking sheets once, until apples are just tender, 25–30 minutes. Let cool, then transfer apples and accumulated juices to a large bowl. Add butter, brown sugar, cinnamon, and 1 heaping Tbsp. flour; toss to combine. Chill at least 1 hour.

Step 4

Let dough sit at room temperature to soften slightly, about 5 minutes. Roll out 1 disk on a lightly floured surface to a 13" round. Transfer to a 9" pie dish. Lift up edges; let dough slump down into dish. Trim, leaving ½" overhang. Roll out remaining disk. Scrape apples into dish and place dough over top; trim, leaving 1" overhang. Fold edge of top crust under bottom crust, press together to seal, and crimp. Cut 8 slits in top to vent, brush with egg, and sprinkle with remaining 2 Tbsp. granulated sugar. Chill pie in freezer until crust is firm, about 30 minutes.

Step 5

Preheat oven to 400°. Place pie on a parchment-lined rimmed baking sheet; bake 30 minutes (crust should be slightly golden). Reduce oven temperature to 350° and continue baking until juices are bubbling and crust is deep golden brown, 50–60 minutes. Transfer to a wire rack; let cool at least 4 hours before slicing. Serve with crème fraîche.

Step 6

Do Ahead: Roasted apples can be made 1 day ahead; keep chilled.