Prepare Filling: Beat first 3 ingredients at medium speed with an electric mixer until blended and smooth. Add egg, flour, and vanilla; beat just until blended.
Prepare Batter: Preheat oven to 350º. Bake pecans in a shallow pan 8 to 10 minutes or until toasted and fragrant, stirring halfway through. Stir together 3 cups flour and next 7 ingredients in a large bowl; stir in eggs and next 3 ingredients, stirring just until dry ingredients are moistened. Stir in apples and pecans.
Spoon two-thirds of apple mixture into a greased and floured 14-cup Bundt pan. Spoon Cream Cheese Filling over apple mixture, leaving a 1-inch border around edges of pan. Swirl filling through apple mixture using a paring knife. Spoon remaining apple mixture over Cream Cheese Filling.
Bake at 350º for 1 hour to 1 hour and 15 minutes or until a long wooden pick inserted in center comes out clean. Cool cake in pan on a wire rack 15 minutes; remove from pan to wire rack, and cool completely (about 2 hours).
Prepare Frosting: Bring 1/2 cup brown sugar, 1/4 cup butter, and 3 tablespoons milk to a boil in a 2-qt. saucepan over medium heat, whisking constantly; boil 1 minute, whisking constantly. Remove from heat; stir in vanilla. Gradually whisk in powdered sugar until smooth; stir gently 3 to 5 minutes or until mixture begins to cool and thickens slightly. Pour immediately over cooled cake.