Preheat oven to 425°. Peel and core apples; cut into 1/2-inch-thick wedges. Place apples in a large bowl. Stir in 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 top sheet of wax paper. Starting at 1 edge of dough, wrap dough around rolling pin, separating dough from bottom sheet of wax paper as you roll. Discard bottom sheet of wax paper. Place rolling pin over a 9-inch glass pie plate, and unroll dough over pie plate. Gently press dough into pie plate.
Stir apple mixture; reserve 1 Tbsp. juices. Spoon apples into crust, packing tightly and mounding in center. Pour remaining juices in 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 dough over filling; fold edges under, sealing to bottom crust, and crimp. Brush top of 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 pie for steam to escape.
Bake at 425° on lower oven rack 15 minutes. Reduce oven temperature to 350°; transfer 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, 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. Serve with Brandy-Caramel Sauce.