10 cups sliced peeled tart apples (about 8 medium)
1 teaspoon lemon juice
1/4 cup sugar
1/4 cup packed brown sugar
3 tablespoons all-purpose flour
1 teaspoon ground cinnamon
1/2 teaspoon ground nutmeg
1 tablespoon butter
1 large egg
1 tablespoon whole milk
Place flour in a large bowl; cut in shortening until crumbly. In a small bowl, whisk egg, water and vinegar; gradually add to crumb mixture, tossing with a fork until dough holds together when pressed. Shape into a rectangle. Wrap and refrigerate 30 minutes or overnight.
Preheat oven to 375°. For filling, in a large bowl, toss apples with lemon juice. In a small bowl, combine sugars, flour, cinnamon and nutmeg; add to apple mixture and toss to coat. Transfer to a 13x9-in. baking dish; dot with butter.
On a lightly floured surface, roll dough to fit top of pie. Place over filling. Trim and flute edges. In a small bowl, whisk egg with milk; brush over crust. Cut slits in top. Bake 40-50 minutes or until crust is golden brown and apples are tender. Cool on a wire rack.