Mix the crushed cookies with melted butter until evenly moistened. Press into the bottom of a 9-inch springform pan. Bake at 325°F (163°C) for 10 minutes. Let cool slightly.
Beat the cream cheese until smooth. Add sugar and mix until combined. Add eggs one at a time, mixing well after each. Stir in vanilla, cinnamon, nutmeg, and sour cream until smooth. Pour over the cooled crust.
Cook apples, sugar, cinnamon, and butter in a pan over medium heat for 5–7 minutes until tender. Spoon evenly over cheesecake batter.
Combine flour, sugar, and cinnamon. Cut in butter with a fork or fingers until mixture resembles coarse crumbs. Sprinkle over the apple layer.
Bake the cheesecake at 325°F (163°C) for 50–60 minutes or until the center is just set. Turn off the oven, crack the door open, and let the cheesecake cool for 1 hour. Then refrigerate for at least 4 hours or overnight.
