Preheat oven to 325°F (160°C). Mix graham cracker crumbs, sugar, and melted butter. Press firmly into a springform pan. Bake for 10 minutes, then cool.

In a bowl, beat softened cream cheese until smooth. Add sugar and vanilla; mix well. Add eggs one at a time, scraping sides between additions. Fold in sour cream. Pour over crust.

In a saucepan, combine apples, brown sugar, cinnamon, cornstarch, water, and lemon juice. Cook for 5 minutes until thickened slightly. Spread the apple mixture over the cheesecake layer.

In another bowl, mix flour, brown sugar, cinnamon, and cubed butter until crumbly. Sprinkle over the apple layer.

Bake cheesecake for 65 minutes in a water bath. Turn off the oven, crack the door, and cool inside for 10 minutes. Remove and cool completely.

Refrigerate for at least 4 hours or overnight before serving.