Dough:

Stir together the first 4 ingredients in a large bowl. Cut butter and shortening into flour mixture with a pastry blender until mixture resembles small peas. Mound mixture on 1 side of the bowl.

Drizzle 1 Tbsp. apple cider along the edge of the mixture in the bowl. Using a fork, gently toss a small amount of flour mixture into cider just until dry ingredients are moistened; move the mixture to another side of the bowl. Repeat the procedure with the remaining cider and flour mixture.

Gently gather the dough into two flat disks. Wrap in plastic wrap, and chill 1 to 24 hours.

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Filling:

Preheat oven to 425F. Peel and core apples; cut into 1/2-inch-thick wedges. Place apples in a large bowl. Stir in the next 7 ingredients. Let stand 30 minutes, gently stirring occasionally.

Place 1 Cornmeal Crust Dough disk on a lightly floured piece of wax paper; sprinkle dough lightly with flour. Top with another sheet of wax paper. Roll dough to about 1/8-inch thickness (about 11 inches wide).

Remove and discard the top sheet of wax paper. Starting at 1 edge of the dough, wrap dough around the rolling pin, separating dough from the bottom sheet of wax paper as you roll. Discard the bottom sheet of wax paper. Place rolling pin over a 9-inch glass pie plate, and unroll dough over the pie plate. Gently press dough into the pie plate.

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Stir apple mixture; reserve 1 Tbsp. juices. Spoon apples into crust, packing tightly and mounding in the center. Pour remaining juices in the bowl over apples. Sprinkle apples with 3 Tbsp. sugar; dot with butter.

Roll remaining Cornmeal Crust Dough disk as directed in Step 2, rolling dough to about 1/8-inch thickness (13 inches wide). Remove and discard wax paper, and place the dough over filling; fold edges under, sealing to bottom crust, and crimp. Brush top of the pie, excluding fluted edges, lightly with reserved 1 Tbsp. juices from apples; sprinkle with 1 tsp. sugar. Place pie on a jelly-roll pan. Cut 4 to 5 slits in top of the pie for steam to escape.

Bake at 425° on the lower oven rack for 15 minutes. Reduce oven temperature to 350°; transfer the pie to middle oven rack, and bake 35 minutes. Cover loosely with aluminum foil to prevent excessive browning, and bake 30 more minutes or until juices are thick and bubbly, the crust is golden brown, and apples are tender when pierced with a long wooden pick through slits in crust. Remove to a wire rack. Cool 1 1/2 to 2 hours before serving.