Preheat oven to 325°F (163°C). Grease and line a 9-inch springform pan.
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Mix graham cracker crumbs, sugar, and melted butter. Press firmly into the bottom of the pan to form the crust.
In a large bowl, beat cream cheese until smooth. Add sugar, then eggs one at a time. Mix in vanilla and sour cream. Pour over crust.
In another bowl, toss sliced apples with brown sugar, cinnamon, and nutmeg. Spread evenly over cheesecake layer.
Make the crisp topping by mixing oats, brown sugar, flour, and butter until crumbly. Sprinkle on top of apples.
Bake for 65–70 minutes, until center is set and topping is golden. Turn off oven, crack the door, and let cheesecake cool inside for 1 hour.
Chill in refrigerator at least 4 hours (overnight is best) before slicing.