Step 1

In small bowl, combine 2 tablespoons granulated sugar, flour, cornstarch, cinnamon, and nutmeg; set aside. In large bowl, combine brown sugar, lemon juice, salt, and 2 tablespoons granulated sugar.

Step 2

Peel, core, and cut apples into 1/2-inch-thick wedges and add to large bowl with brown sugar mixture. Macerate, tossing a few times, until juicy, about 15 minutes.

Step 3

Melt butter in large skillet over medium, then add apples and all their juices. Cover and cook, stirring occasionally, 5 minutes. Uncover, stir in cranberries, and continue to cook, uncovered, until apples are just tender but not mushy and cranberries have released their juices, 5 to 7 minutes. Lower heat, sprinkle in spiced flour, and cook, stirring, until thickened, 1 minute. Transfer mixture and all its juices into heatproof bowl and let cool, about 1 hour.

Step 4

Heat oven to 400°F. Let dough soften slightly at room temperature, 5 to 10 minutes. On lightly floured sheet of parchment, with floured rolling pin, roll 1 disk of dough to about 12-inch round. Freeze until very firm, 15 minutes. Meanwhile, on lightly floured work surface, roll remaining disk to about 12-inch round and fit into bottom and up sides of 9-inch pie plate.

Step 5

Remove dough from freezer, cut into 21/2-inch squares, and let soften just until flexible. Arrange on top of pie filling, nearly touching, letting some overlap on crust. If necessary, trim overhang to 1 inch all around. Fold edge under itself and crimp as desired.

Step 6

Freeze until firm, 15 minutes. Lightly brush squares and edges with egg and sprinkle with remaining tablespoon sugar. Place on baking sheet and bake until beginning to turn golden brown, 18 to 20 minutes. Tent edges with foil and lower oven temp to 375°F; bake until center of pie begins to bubble, 30 to 35 minutes more (tent entire pie during last 10 minutes if necessary to prevent burning). Let cool at least 2 hours before slicing.