1-Prepare the crust: Preheat oven to 325°F (160°C). Combine graham cracker crumbs, brown sugar, and melted butter until evenly moistened. Press firmly into the base and slightly up the sides of a lined 8 or 9-inch springform pan. Bake 10–12 minutes until lightly golden. Cool completely.

2-Prepare the apple crumble topping: Peel and finely chop apples. Mix flour, brown sugar, cinnamon, and nutmeg (if using). Add room temperature butter and crumble using fingertips or mixer. Toss 1 cup of mixture with chopped apples and refrigerate separately.

3-Optional caramel apple filling: Cook sliced apples with brown sugar, cinnamon, and nutmeg over medium heat for 6–7 minutes until tender but not mushy. Cool for later use.

4-Make cheesecake batter: Beat cream cheese on medium until smooth (about 2 minutes). Gradually add brown and granulated sugar, beat another 2 minutes. Add sour cream and applesauce, mix until smooth. Add eggs one at a time, mixing gently after each. Add egg yolk, vanilla, salt, cinnamon, and optional flour or cornstarch, mix until combined.

5-Assemble cheesecake: Wrap springform pan bottom tightly with foil to prevent water leakage. Pour half the batter over cooled crust, spread evenly. Layer half the apple crumble mixture over batter. Add remaining batter, followed by rest of apple crumble. Sprinkle reserved crumble evenly on top.

6-Bake in water bath: Set springform pan in larger roasting pan. Pour hot water halfway up sides of springform pan. Bake at 325°F (160°C) for 60–75 minutes until edges are set and center jiggles slightly. Tent with foil if browning too fast.

7-Cool gradually: Turn off oven and leave cheesecake inside with door closed for 1 hour. Remove from water bath and cool completely on wire rack. Refrigerate minimum 6 hours or overnight.

8-Serve: Drizzle with salted caramel sauce if desired. For neat slices, use serrated knife for crumb and sharp chef’s knife for cheesecake.