To prepare crust, lightly spoon flour into dry measuring cups; level with a knife. Combine 1/3 cup flour and ice water, stirring with a whisk until well-blended. Combine 1 2/3 cups flour and salt in a bowl; cut in margarine and shortening with a pastry blender or 2 knives until mixture resembles coarse meal. Add ice water mixture; toss with a fork until moist. Divide dough in half. Gently press each half of mixture into a 4-inch circle on heavy-duty plastic wrap, and cover with additional plastic wrap. Roll one half of dough, still covered, into a 12-inch circle, and chill. Roll other half of dough, still covered, into an 11-inch circle; chill.
To prepare filling, bring cider to a boil in a large, heavy saucepan over high heat. Cook until reduced to 1/2 cup (about 20 minutes). Cool completely.
Preheat oven to 450°.
Combine cooled cider, 1/3 cup sugar, cornstarch, lemon juice, vanilla, and pie spice in a large bowl. Cut each apple quarter crosswise into 1/4-inch-thick slices. Stir apple slices into cider mixture.
Remove 1 sheet of plastic wrap from the 12-inch circle; fit dough into a 9-inch pie plate coated with cooking spray, allowing dough to extend over edge of plate. Remove top sheet of plastic wrap. Spoon apple mixture into crust, and brush edges of crust lightly with water. Remove 1 sheet of plastic wrap from the 11-inch circle, and place on top of apple mixture. Remove top sheet of plastic wrap. Press edges of dough together; fold edges under, and flute. Cut 6 (1-inch) slits into top of pastry using a sharp knife. Combine egg and 1 tablespoon water. Brush top and edges of pie with egg mixture, and sprinkle with 1 tablespoon sugar. Place pie on a baking sheet, and bake at 450° for 15 minutes. Reduce oven temperature to 350° (do not remove pie from oven), and bake an additional 45 minutes or until golden. Cool on a wire rack.