Three different types of apples and fresh cranberries, baked together under a perfectly woven lattice crust. This pie is as delicious as it is gorgeous.
Prepare the Crust: Pulse flour, granulated sugar, and salt in a food processor until combined, 2 to 3 times. Scatter butter and shortening over flour mixture; pulse until mixture resembles coarse sand, 4 to 5 times. Sprinkle ice water over top; pulse until mixture starts to clump, 4 to 5 times. Transfer mixture to a lightly floured work surface; knead until dough comes together, 4 or 5 times. Wrap one-third of dough with plastic wrap; wrap remaining dough with plastic wrap. Chill 1 hour.
Meanwhile, prepare the Filling: Toss together apples, cranberries, and lemon juice in a large bowl. Add granulated sugar, brown sugar, flour, salt, nutmeg, and cinnamon; toss well to coat. Let stand while dough is chilling.
Preheat oven to 400°F, with rack in lowest third of oven.
Lightly coat a 15- x 10-inch rimmed baking sheet with cooking spray. Unwrap larger dough portion, and roll into a 17- x 12-inch rectangle on a lightly floured surface. Fit dough into bottom and up sides of prepared baking sheet. Tuck edges under and crimp.
Unwrap smaller dough portion, and roll into a 15- x 8-inch rectangle. Using a fluted dough cutter, cut dough lengthwise into 16 (15- x 1/2-inch) strips. Transfer apple mixture to piecrust, lightly pressing to flatten surface. Arrange dough strips across top of pie in a lattice pattern. Gently press ends of strips with a fork, sealing to bottom crust. Cut off and discard any excess dough.
Using a fork, stir together egg yolk and water in a small bowl. Brush egg mixture on edges of piecrust and across lattice.
Bake pie on lowest rack in preheated oven 15 minutes. Without removing pie from oven, reduce heat to 350°F. Bake until golden brown and bubbly, 40 to 45 more minutes. (Shield edges with aluminum foil after 30 minutes, if necessary, to prevent excessive browning.) Serve warm, or cool completely on a wire rack, about 1 hour.