Preheat oven to 350.
Grease bottom and sides of springform pan (I used 9"). Set aside.
In a medium bowl, whisk together flour, baking soda, cinnamon and nutmeg. Set aside.
In large bowl, Beat together applesauce (or oil), sugar, eggs and vanilla until well blended.
Add dry ingredients to wet ingredients and mix well.
Stir in shredded apples.
Set aside cake batter.
In large bowl, beat together cream cheese, sugar and vanilla until smooth.
Beat in eggs until smooth.
Set aside cheesecake batter.
Spread 2 cups of cake batter over bottom of prepared pan.
Place spoonfuls of cheesecake batter in pan.
Top with spoonfuls of remaining cake batter.
Top with spoonfuls of remaining cheesecake batter and gently smooth top with a knife.
Bake for 55-65 minutes or until cake is set and cooked throughout.
Allow to cool to room temperature, then refrigerate 30 minutes.
Beat butter and cream cheese in large bowl until light and fluffy.
Add in powdered sugar and caramel and beat on high until smooth.
Frost top and sides of cheesecake. I used star tip around edges.
Top with apple pie filling and drizzle with caramel if desired.
Refrigerate several hours before serving.