Line the bottom of a 9 inch spring-form pan with parchment paper and grease the sides. Adjust an oven rack to the center position and preheat the oven to 350°.
For the apple-spice blondie base: In a microwave safe bowl, melt the butter using 10-second increments. Transfer the melted butter to a large mixing bowl. Add the brown sugar and whisk to combine. Add the vanilla, egg and egg white and whisk until incorporated.
In a medium mixing bowl, whisk together the flour, cinnamon, apple pie spice, baking powder, baking soda and salt. Slowly add the dry ingredients to the wet ingredients, stirring until combined. Fold in the chopped apple. Pour this batter into your prepared pan and bake it for 30-33 minutes. Allow it to cool for about 5 minutes, then remove the blondie to a cooling rack to finish cooling.
Meanwhile, make the caramel sauce: In a medium saucepan over medium heat, melt the butter. Add the brown sugar and heavy cream and whisk constantly over medium heat until sugar is dissolved. Bring the pan to a boil and allow it to boil for 3 minutes, no more. Remove the pan from the heat and allow it to cool completely. You can store the caramel in refrigerator.
Once the blondie and caramel are cool, make the cheesecake: In a large mixing bowl or the bowl of a stand mixer, mix the cream cheese, white sugar and brown sugar until smooth. Add 3/4 cup of the caramel sauce and apple pie spice and mix until well combined. Fold in the Cool Whip. Place the blondie back into the spring-form pan. Spread cheesecake mixture evenly on top of the blondie base, then put it in the refrigerator until it is firm, 3-4 hours.
In a medium mixing bowl, combine the apple slices, lemon juice, nutmeg, cinnamon and brown sugar in a medium saucepan, tossing to coat. Add the butter and cook over medium-high for about 15-20 minutes, until the apples have softened. Cool them for 10-15 minutes, then place them on top of the cheesecake.
Make the cinnamon whipped cream: Freeze a metal bowl and whisk attachment for 10-15 minutes. Remove bowl from freezer, add the heavy cream, and whip on high speed until it begins to thicken. Add the powdered sugar and cinnamon and whip until it you get stiff peaks.
Pipe the whipped cream around the edges of your cheesecake. Drizzle more caramel sauce over finished cheesecake.