In the bowl of your stand mixer, blend the cream cheese, brown sugar, flour, and cinnamon on low speed until well combined and smooth. Make sure to use low speed while beating to avoid adding excess air, which will cause the cheesecake to crack.
Scrape down the sides of the bowl. Add in the sour cream, heavy whipping cream, applesauce, and caramel sauce until well combined. Add the eggs one at a time, mixing slowly to combine. Scrape down the sides of the bowl as needed to make sure everything is mixed. Pour the cheesecake filling into the crust.
Place the cheesecake pan in a larger roasting pan. Place the pan in the oven and then fill the pan with enough warm water to go about halfway up the side of the springform pan. The water should not go above the top of the foil. Bake the cheesecake for 1 hour and 25 minutes.
Turn off the oven and leave the cheesecake in the oven with the door closed for 30 minutes. Do not open the door! After 30 minutes, crack the oven door and leave the cheesecake in the oven for another 20 minutes. Take the cheesecake out of the oven and let it sit at room temperature for 15 minutes, then remove the pan from the water bath and remove the foil. Wrap it with plastic wrap and refrigerate until it's completely cool and firm, 6-7 hours or overnight.
Don't remove the springform pan from the cheesecake until it's done chilling and you're ready to assemble.