Preheat oven to 325°F (160°C). In a small bowl, mix graham cracker crumbs, brown sugar, and melted butter. Press mixture into a 9-inch springform pan.
In a large bowl, beat cream cheese, granulated sugar, and vanilla until smooth. Add eggs one at a time, mixing well after each. Pour mixture into prepared crust and bake for 45-50 minutes. Let cool.
To make caramel sauce: Combine butter, brown sugar, corn syrup, and salt in a saucepan. Cook over medium heat until golden. Remove from heat, stir in heavy cream, then vanilla. Pour over cooled cheesecake. Top with apple slices and chill for 4-6 hours before serving.
Before serving, garnish with additional caramel drizzle and whipped cream if desired.