Preheat oven to 325°F (163°C). Grease a 9-inch springform pan.

Combine graham cracker crumbs, sugar, and melted butter in a bowl. Press into pan bottom and bake for 10 minutes. Cool slightly.

Beat cream cheese until smooth, add sugar, and mix well. Add eggs one at a time, then vanilla and sour cream. Mix until just combined.

Pour filling over crust. Place springform in a larger pan with hot water halfway up sides (water bath).

Bake 55–65 minutes until center is almost set. Turn off oven, crack door, and cool for 1 hour. Chill 4 hours or overnight.

For topping, melt butter in skillet, add apples, brown sugar, cinnamon, and nutmeg. Cook until soft and syrupy, about 8 minutes. Cool.

For caramel, melt sugar in a saucepan until amber. Add butter and stir until melted. Slowly pour in cream, boil 1 minute, then add salt. Cool slightly.

Top chilled cheesecake with apple mixture and drizzle with caramel before serving.