Preheat the oven to 325°F (160°C).
Combine graham cracker crumbs and melted butter in a bowl.
Press the mixture into the bottom of a springform pan to create the crust.
Bake the crust for 10 minutes, then set aside to cool.
In a large bowl, beat the softened cream cheese until smooth.
Add 1/2 cup of sugar, eggs, and vanilla extract to the cream cheese, blending well.
Pour the cheesecake mixture over the baked crust.
In another bowl, toss sliced apples with 1/2 cup sugar, flour, and cinnamon.
Spread the spiced apple mixture over the cheesecake layer.
Prepare the crumble by mixing oats, brown sugar, and additional flour together.
Sprinkle the crumble mixture over the apple layer.
Bake the cheesecake for 50-60 minutes or until the edges are set.
Let the cheesecake cool completely before removing from the pan.
Chill in the refrigerator for at least 4 hours, preferably overnight, before serving.
