Preheat your oven to 160ºC (325ºF). In a food processor, blend the digestive or graham crackers, dark brown sugar, ground cinnamon, and nutmeg until finely crushed. Pour in the melted butter, mixing until the mixture is crumbly and sticks together. Firmly press the mixture into the bottom and sides of a springform pan. Bake for 10 minutes, then let it cool while you prepare the other layers.

Dice the apples into small pieces and toss them in a bowl with granulated sugar and a sprinkle of ground cinnamon until evenly coated. In another bowl, combine all-purpose flour, brown sugar, and room-temperature butter. Use your fingers or a fork to mix until the mixture resembles coarse crumbs. Set both the apples and crumble topping aside while you make the cheesecake filling.

In a large mixing bowl, beat the cream cheese with an electric mixer until smooth and creamy, about 2 minutes. Gradually add the granulated sugar, mixing until well combined. Mix in the sour cream combined with cornstarch, followed by the vanilla extract. Add the eggs one at a time, ensuring each is fully blended before adding the next.

Pour the cheesecake filling into the cooled crust, smoothing it out evenly. Layer the sautéed apples on top of the filling, distributing them evenly. Sprinkle the crumble topping generously over the apples. Place your springform pan into a larger baking dish filled with hot water, creating a water bath to help prevent cracking. Bake in the preheated oven for 1 hour and 20-30 minutes.

After baking, turn off the oven and leave the cheesecake inside with the door slightly ajar for about 1 hour. This gradual cooling process helps stabilize the cheesecake. Allow it to cool completely at room temperature, then refrigerate for at least 6 hours, or ideally overnight, before serving.