Preheat oven to 350 degrees F. In a large bowl combine flour, the 2 Tbsp. sugar, and the salt. Using a pastry blender, cut in shortening and butter until pieces are pea-size. Sprinkle 1 Tbsp. of the ice water over part of the flour mixture; toss gently with a fork. Push moistened dough to side of bowl. Repeat moistening flour mixture, using 1 Tbsp. of the ice water at a time, until all of the flour mixture is moistened. Shape two-thirds of the dough into a ball. Shape the remaining dough into a smaller ball.
Place the larger ball of dough between two pieces of lightly floured waxed paper. Roll dough to a 17x12-inch rectangle. Remove top piece of waxed paper. Carefully invert pastry into a 15x10-inch baking pan. Peel off waxed paper. Press dough up sides of pan; trim edges (if needed, use trimmed pieces to patch any holes). Top with thinly sliced apples. In a small bowl combine the 1 1/4 cups sugar and the cinnamon. Set aside 1/3 cup of the cinnamon-sugar mixture. Sprinkle the remaining cinnamon-sugar mixture over apples. Place the remaining dough between two pieces of lightly floured waxed paper; roll into a 16x11-inch rectangle. Remove top piece of waxed paper. Invert pastry over apple layer. Peel off waxed paper. Using your fingers, seal edges of pastry together; use a fork to crimp edges. Cut slits in the top pastry for steam to escape. In a small bowl whisk together egg white and 1 Tbsp. cold water; brush over pastry. Sprinkle reserved cinnamon-sugar mixture evenly over pastry.
Bake about 45 minutes or until pastry is golden brown and apples are tender. Cool in pan on a wire rack.