Heat oven to 325 degrees Fahrenheit and grease a 9-inch pie dish.
Mix graham crumbs, melted butter, and brown sugar, pressing firmly into pie dish bottom and sides.
Beat cream cheese and sugar until creamy, then blend in eggs and vanilla on low speed.
Pour filling into crust and bake for 50 minutes until center is almost set, then chill for 3 hours.
Cook sliced apples, butter, brown sugar, and cinnamon in a skillet for 8 minutes until tender.
Cool apples, arrange over chilled cheesecake, and drizzle with warm caramel sauce.