Pour the sugar in an even layer in a large saucepan. Heat the sugar over medium-high heat, whisking the sugar until melted. The sugar will clump up first, but will eventually completely melt after about 10 to 15 minutes.
Once the sugar has melted, stop whisking and allow the sugar to cook until it has turned a little darker amber color. You may notice a nutty aroma. The change in color will happen quickly so don't let it go too long or get too dark or it will burn. Turn off the stove but leave the caramel over the heat.
Slowly add the butter and whisk until combined. It is very important that the butter is room temperature or warmer. If it's too cold, the caramel will seize. The mixture will bubble up, but keep whisking until all the butter has melted and combined.
Slowly pour the heavy whipping cream into the caramel and whisk constantly until incorporated. Again temperature is very important. If it's too cold, the caramel will seize. Set the caramel aside to cool.
For the Crust:
Preheat oven to 325°F. Line the bottom of a 9-inch springform pan with parchment paper and grease the sides.
To make the crust, combine the vanilla wafer crumbs, butter, and brown sugar in a small bowl and stir with a fork to combine. Press into the bottom and up the sides of the pan. Bake the crust for 10 minutes, then set aside to cool. Cover the outside of the pan with aluminum foil so that water from the water bath cannot get in. Set the prepared pan aside. Reduce the oven temperature to 300°F.
For the Cheesecake Filling:
In a large bowl, 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, 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.
For the Cinnamon Apples:
Combine apples, brown sugar, lemon juice, cinnamon, and butter in a large saucepan. Cook over medium heat until the apples are tender, about 10-15 minutes.
Spread the top of the cheesecake with additional caramel sauce, then spoon the apples over the top in the center. Drizzle additional caramel down the sides of the cheesecake if desired. Refrigerate cheesecake until ready to serve.
It's best eaten within 2-3 days but should last 4-5 days.