In a small bowl, whisk together 1/4 cup all-purpose flour, ice water, and vinegar until well blended. In a large bowl, combine remaining 1/4 cup all-purpose flour, whole wheat flour, confectioners sugar and salt. Cut in shortening with 2 knives until mixture resembles coarse meal. Add vinegar mixture and toss with a fork until moist. Press dough into a circle and chill, covered tightly with plastic wrap, for 10 minutes.

Preheat oven to 425°. Lightly coat a 9-inch deep-dish pie plate with nonstick cooking spray.

In a large bowl, combine apples and lemon juice and toss. In a small bowl, combine 1/3 cup sugar, flour, cinnamon and nutmeg. Sprinkle sugar mixture over apples and toss well to coat evenly. Mix in the cornstarch and transfer filling to pie plate.

Roll out dough on a lightly floured surface with a lightly floured rolling pin and fit over pie plate. Trim edge, leaving a 1/2-inch overhang. Fold the overhang over, pressing over the edge of the pie plate to seal it, and crimp the edge. With a sharp knife, cut slits in dough to form 3 or 4 steam vents. Brush the crust with milk and sprinkle with 1 tablespoon sugar. Bake pie in the middle of the oven for 15 minutes. Reduce the temperature to 350°, cover loosely with foil and bake for 45 minutes, or until the crust is golden. Cool for at least 1 hour on a wire rack.