1. Preheat oven to 350°. Bake pecans in a single layer in a shallow pan 8 to 10 minutes or until lightly toasted and fragrant, stirring halfway through. Reduce oven temperature to 325°. Sprinkle pecans over bottom of a greased and floured shiny 9-inch springform pan.
2. Beat cream cheese, granulated sugar, and vanilla at medium speed with a heavy-duty electric stand mixer until blended and smooth. Add 3 eggs, 1 at a time, beating just until blended after each addition.
3. Whisk together brown sugar, melted butter, and remaining egg in a large bowl until blended.
4. Stir together flour and next 3 ingredients; add to brown sugar mixture, and stir until blended. Stir in apples. Spoon batter into prepared pan. Carefully spoon cream cheese mixture over batter.
5. Bake at 325° for 1 hour and 10 minutes or until set. Remove from oven, and gently run a knife around outer edge of cheesecake to loosen from sides of pan. (Do not remove sides of pan.) Cool completely in pan on a wire rack (about 2 hours). Transfer to a serving plate.
6. Meanwhile, prepare Caramel Apple Topping and Caramel Sauce. Reserve 1 cup Caramel Sauce for another use. Spoon topping over cheesecake; drizzle with 1/2 cup Caramel Sauce.