Preheat oven to 325°F (163°C). Combine crust ingredients and press into a springform pan. Bake 10 minutes, then cool.
Cook apples with butter, brown sugar, cinnamon, and nutmeg until softened. Add cornstarch mixture to thicken, then cool.
Beat cream cheese until smooth, add sugar, eggs, sour cream, vanilla, and caramel until combined.
Pour half the cheesecake batter over crust, add apple mixture, then remaining batter.
Bake 55–65 minutes until center is set. Cool in oven 1 hour, then refrigerate 6 hours or overnight.
Before serving, drizzle with salted caramel and sprinkle sea salt.