Preheat the oven to 320°F.
Beat the cream cheese on low speed, then gradually add the granulated sugar.
Scrape down the sides of the bowl and continue mixing on low speed for another minute.
In a separate bowl, mix the sour cream and cornstarch until smooth.
Add the sour cream mixture and vanilla extract to the cream cheese, then beat on low speed until fully combined.
Add the eggs one at a time, mixing on low speed after each addition.
Once all the eggs are added, scrape down the sides of the bowl and beat the batter one final time to ensure everything is well incorporated.
Pour the cheesecake batter over the prepared crust.
Scatter the cinnamon sugar apples evenly over the cheesecake layer, then sprinkle the crumble on top.
To prepare a water bath, place the springform pan inside a cake pan, then set that inside a larger roasting pan.
Fill the roasting pan with hot water until it reaches about halfway up the sides of the cake pan.
Bake the apple crumble cheesecake for 1 hour and 25 minutes, or until the center is slightly wobbly.
Turn off the oven and crack the door open slightly. Let the cheesecake cool inside the warm oven for 1 hour.
Transfer the cheesecake to a cooling rack and let it come to room temperature, about 1 hour.
Refrigerate the cheesecake for at least 6 hours, or preferably overnight, before serving.