Prepare the apple filling by peeling, coring, and slicing apples. Melt butter and cook with brown sugar, cinnamon, lemon juice, and nutmeg for 5-7 minutes until tender.

Make the crust by mixing graham cracker crumbs, sugar, and cinnamon with melted butter. Press into a springform pan and bake at 350°F for 7-8 minutes.

In a mixing bowl, beat cream cheese with sugar, vanilla, and cinnamon until smooth. Blend in sour cream and eggs, followed by cornstarch until lumps disappear.

For the crumble topping, mix flour, oats, brown sugar, cinnamon, and salt, then combine with melted butter until crumbly.

Assemble the cheesecake by pouring half the filling into the crust, adding apple filling, and then remaining cheesecake batter. Top with crumble.

Bake at 300°F for about 60 minutes until edges are set. Let it cool in the oven for 1-2 hours.

Chill in the refrigerator for at least 5 hours or overnight before serving.