Peel, core, and slice the apples into medium-sized slices, ensuring they are not too thin. Using an apple peeler and corer can help speed up this process. In a saucepan over medium heat, combine the butter, water, brown sugar, cinnamon, lemon juice, vanilla extract, nutmeg, and kosher salt. Stir with a wooden spoon until the butter is fully melted. Add the sliced apples and gently mix to avoid breaking them. Reduce the heat to medium-low, cover with a lid, and cook for approximately 10 minutes, or until the apples soften. Stir in the cornstarch mixture (cornstarch dissolved in a small amount of water) and mix until smooth with no visible lumps. Set aside to cool completely.

Line a 10-inch springform pan with parchment paper and preheat the oven to 180°C (350°F). Process the graham crackers in a food processor until fine crumbs form. If a food processor is unavailable, place the crackers in a Ziplock bag and crush them into fine crumbs using a cup. In a medium mixing bowl, combine the graham cracker crumbs, granulated sugar, cinnamon, and melted butter. Stir until the crumbs are evenly coated. Transfer the mixture to the prepared pan and press it firmly and evenly into the bottom. Bake the crust in the preheated oven for 7-8 minutes, watching closely to prevent burning. Remove from the oven and allow it to cool to room temperature.

Reduce the oven temperature to 140°C (280°F). In a large mixing bowl, combine the room-temperature cream cheese, granulated sugar, and vanilla extract. Beat with an electric hand mixer until the mixture is smooth and creamy. Add the sour cream and mix until fully combined. In a separate bowl, whisk the eggs, then gradually add them to the cheesecake mixture, blending until smooth. Sift in the cornstarch and mix until fully incorporated, ensuring there are no lumps.

In a medium mixing bowl, combine the flour, oats, brown sugar, kosher salt, cinnamon, and melted butter. Stir until the mixture is evenly combined and forms a crumbly texture.

Pour half of the cheesecake mixture over the cooled crust, then gently layer the apple filling on top. Spread the remaining cheesecake mixture over the apple layer, and finish by evenly sprinkling the crumble topping over the surface. Bake the assembled cheesecake in the preheated oven at 140°C (280°F) for approximately one hour, or until the edges are set but the center remains slightly jiggly. Turn off the oven, crack the door open halfway, and allow the cheesecake to cool to room temperature for 1-2 hours. Once cooled, tightly wrap the cheesecake with plastic wrap and refrigerate for at least 5 hours to set completely.

Carefully release the cheesecake from the springform pan. Before serving, drizzle with caramel sauce or dust generously with powdered sugar, if desired.