In a medium saucepan, melt 2 tablespoons of butter over medium heat. Add peeled and chopped apples, ¼ cup of brown sugar, ½ teaspoon of cinnamon, and 1 tablespoon of lemon juice. Cook for 8-10 minutes until the apples are fork-tender. Mix 1 tablespoon of cornstarch with 2 tablespoons of water, add to the apples, and stir until thickened. Remove from heat and let cool.

Preheat your oven to 350°F (175°C). In a mixing bowl, combine 1 ½ cups of graham cracker crumbs, ¼ cup of granulated sugar, and ½ teaspoon of cinnamon. Pour in 6 tablespoons of melted unsalted butter and mix until crumbly. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 8-10 minutes or until lightly golden and fragrant, then set aside to cool.

In a large mixing bowl, beat 16 ounces of room temperature cream cheese and ¾ cup of granulated sugar with an electric mixer until smooth, usually about 2-3 minutes. Slowly add in 1 teaspoon of vanilla extract, then add 3 large eggs one at a time, mixing gently to avoid incorporating too much air. Finally, blend in ½ cup of sour cream and 2 tablespoons of cornstarch until fully combined and smooth.

Spoon half of the cheesecake filling onto the cooled graham cracker crust. Spread it evenly, followed by the cooled apple filling, which adds a comforting layer to the dessert. Pour the rest of the cheesecake batter over the apple filling, smoothing the top. Finish by sprinkling the crumble topping evenly across the surface to create that delicious crunchy layer.

Lower the oven temperature to 325°F (160°C). Place the assembled cheesecake in the preheated oven and bake for 50-60 minutes. The edges should be set while the center will slightly jiggle when nudged.

Once baked, turn off the oven and leave the cheesecake inside with the door slightly ajar for about 1 hour. This gradual cooling helps prevent cracks. Afterward, transfer it to the refrigerator to chill for a minimum of 5 hours or overnight for best results.

Carefully remove the cheesecake from the springform pan. For an extra special touch, drizzle with warm caramel sauce and add optional garnishes like whipped cream or a scoop of vanilla ice cream.