Prepare Cake: Preheat oven to 350°. Beat first 2 ingredients at medium speed with a heavy-duty electric stand mixer until light and fluffy. Add eggs, 1 at a time, beating just until blended after each addition; stir in vanilla.
Whisk together flour and next 4 ingredients in a medium bowl. Add flour mixture to sugar mixture alternately with buttermilk, beginning and ending with flour mixture. Beat just until blended after each addition. Spread batter in a greased (with shortening) and floured 9- x 2-inch round cake pan.
Bake at 350° for 50 minutes or until a wooden pick inserted in center comes out clean, shielding with aluminum foil after 35 to 40 minutes to prevent excessive browning, if necessary. Cool in pan on a wire rack 10 minutes. Remove from pan, and cool completely (about 1 hour).
Meanwhile, prepare Apples. Cut apples into 1/2-inch-thick wedges. Toss together apples, 1/2 cup brown sugar, and next 3 ingredients. Melt 2 Tbsp. butter in a large skillet over medium-high heat; add apple mixture, and sauté 5 to 6 minutes or until crisp-tender and golden. Cool completely (about 30 minutes).
Arrange sautéed apples over cooled cake, and drizzle with desired amount of warm Apple Brandy-Caramel Sauce; serve with remaining sauce.