Peel, core, and slice your Granny Smith apples, then place them in a medium saucepan over medium heat. Add butter, brown sugar, cinnamon, and lemon juice, cooking for about 10 minutes until the apples are softened and caramelized.

In a food processor, pulse the graham crackers into fine crumbs. Combine these crumbs with granulated sugar and melted butter in a mixing bowl, stirring until fully combined. Press this mixture firmly into the bottom of a 10-inch springform pan, creating an even layer. Bake in a preheated oven at 350°F (175°C) for 7-8 minutes, then set aside to cool completely.

In a large mixing bowl, beat the room-temperature cream cheese with granulated sugar and vanilla extract until smooth and creamy, about 3-5 minutes. Add the sour cream, incorporating it well. Gradually mix in the eggs, one at a time, ensuring each is fully blended before adding the next. Finally, sift in cornstarch and mix until the filling is smooth.

In a separate bowl, combine flour, oats, brown sugar, kosher salt, and cinnamon. Drizzle melted butter over the mixture, using a fork to mix until you achieve a crumbly texture.

Pour about half of the cheesecake filling onto the cooled crust, smoothing it out with a spatula. Layer the cooled apple filling evenly over this layer. Gently pour the remaining cheesecake filling on top, covering the apples completely. Sprinkle the crumble topping generously over the entire cheesecake mixture.

Bake at 280°F (140°C) for approximately 1 hour, or until the edges are set, but the center slightly jiggles.

Once baked, turn off the oven and leave the cheesecake inside with the door slightly cracked for about 1-2 hours to cool gradually.

Refrigerate the cheesecake for at least 5 hours or overnight for best flavor and texture before serving.