In a bowl, combine graham cracker crumbs, melted butter, and brown sugar.

Press the mixture into the bottom of a springform pan to form a crust.

Bake at 350°F (175°C) for 10 minutes.

Let the crust cool to room temperature.

In a skillet, melt butter over medium heat.

Add diced apples, cinnamon, nutmeg, and brown sugar.

Cook until apples are tender, about 5 minutes.

Let the apple mixture cool slightly.

In a bowl, mix flour, oats, and brown sugar.

Add cold butter and use a fork or pastry cutter to create a crumbly texture.

Refrigerate the crumble mixture until ready to use.

In a large bowl, beat softened cream cheese and granulated sugar until smooth.

Add eggs one at a time, mixing well after each addition.

Stir in vanilla extract.

Pour half of the cheesecake filling over the cooled crust.

Evenly distribute the apple filling over the cheesecake layer.

Pour the remaining cheesecake filling over the apples.

Sprinkle the chilled crumble topping over the final layer.

Place the cheesecake in a preheated oven at 325°F (165°C).

Bake for 50-60 minutes, or until the center is set and the topping is golden brown.

If the topping browns too quickly, cover loosely with foil.

Allow the cheesecake to cool to room temperature.

Refrigerate for at least 4 hours, or overnight, to fully set.

Slice and serve chilled, optionally drizzled with caramel sauce or topped with whipped cream.