Preheat oven to 350°F (175°C). Wrap a 9-inch springform pan with two layers of heavy-duty foil. Combine graham cracker crumbs, sugar, and melted butter. Press into the bottom and slightly up the sides of the pan. Bake for 10 minutes. Cool completely.

Reduce oven to 325°F (163°C). Beat room temperature cream cheese until smooth. Add sugars and beat until combined. On low speed, add eggs one at a time. Gently stir in sour cream, heavy cream, flour, and vanilla.

Pour batter into the crust. Place in a large roasting pan and add boiling water halfway up the sides of the springform pan. Bake for 60-70 minutes until the center is almost set. Turn off the oven and let it cool inside with the door cracked for 1 hour.

Remove from the water bath and cool completely at room temperature. Cover and chill in the refrigerator for at least 6 hours or overnight.

While the cheesecake chills, melt butter in a skillet. Add diced apples, brown sugar, cinnamon, and lemon juice. Cook until apples are tender, about 8-10 minutes. Cool completely.

In a saucepan, cook sugar and water over medium-high heat until amber. Do not stir. Remove from heat and slowly whisk in heavy cream, then butter and salt until smooth. Let cool slightly.

Spread the cooled apple topping over the chilled cheesecake. Drizzle with caramel sauce just before serving.