Preheat oven to 325 degrees. Coat a 9 inch bundt pan with nonstick baking spray.
In medium bowl mix flour, baking soda, salt and cinnamon. Set aside.
In stand mixer using paddle attachment beat cream cheese and 2 tablespoons sugar until smooth and creamy; scraping down the sides and beater. Add 1 egg and beat just until incorporated. Set aside.
In large bowl with spoon mix 1 cup sugar, 1/2 cup brown sugar, vegetable oil, applesauce, 1 teaspoon vanilla extract and 3 eggs. Add the flour mixture to the egg/vegetable oil mixture 1/3 at a time; mixing just until incorporated. Fold in chopped apples. Pour 1/2 of the batter into the bundt pan. Spoon the cream cheese mixture one spoonful at a time making a ring around the cake trying to avoid the outside and the inside of the pan. Gently spoon the rest of the apple batter into the cake pan covering up the cream cheese and being careful to seal the cream cheese in.
Bake for 70 minutes. Allow to cool for 15-20 minutes before inverting on to a platter.
Combine 1/2 cup brown sugar, 2 tablespoons butter, 1/2 teaspoon vanilla and half n half in saucepan over medium heat. Cook for 5-7 minutes whisking constantly. Cool slightly before drizzling over cooled cake.
Honeycrsip, Jonagold and Braeburn apples also work well. You want to cool the caramel sauce to drizzling consistency. Just practice to see if it is ready. .