To prepare crust, lightly spoon 2 cups flour into dry measuring cups; level with a knife. Combine with 1/2 teaspoon salt in a bowl; cut in butter and shortening with a pastry blender or 2 knives until mixture resembles coarse meal. Add vinegar and enough ice water, 1 tablespoon at a time, tossing with a fork until dough is moist. Divide dough in half. Gently press each dough half 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; chill. Roll other half of dough, still covered, into an 11-inch circle; chill.
Preheat oven to 450°.
To prepare filling, combine apples and lemon juice in a large bowl. Combine 1/2 cup granulated sugar, brown sugar, 3 tablespoons flour, cinnamon, and 1/4 teaspoon salt. Sprinkle over apple mixture, tossing well to combine.
Remove 1 sheet of plastic wrap from the 12-inch circle; fit dough, plastic-wrap side up, 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. Remove 1 sheet of plastic wrap from the 11-inch circle, and place dough, plastic-wrap side up, 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. Brush top and edges of pie with milk; sprinkle with 1 tablespoon granulated sugar. Place pie on a baking sheet; bake at 450° for 15 minutes. Reduce oven temperature to 375° (do not remove pie from oven). Bake an additional 45 minutes or until golden (shield crust with aluminum foil if it gets too brown). Cool on a wire rack.