In a medium saucepan, combine 0.25 cup of brown sugar and 1 tablespoon of water over medium heat, cooking without stirring for about 10 minutes until deep amber color. Whisk in 6 tablespoons of unsalted butter, followed by ⅔ cup of cold heavy cream and 2 teaspoons of vanilla extract. Set aside to cool.

In a large mixing bowl, beat 16 oz of room-temperature cream cheese and 0.5 cup of brown sugar together until smooth. Gradually add 2 teaspoons of vanilla extract, then slowly pour in ⅔ cup of cold heavy cream while whipping until thickened. Fold in cooled caramel sauce and pour into the graham cracker crust; refrigerate for at least 4 hours.

Melt 2 tablespoons of unsalted butter in a saucepan over medium heat. Add chopped Honeycrisp apples, 0.25 cup of brown sugar, 1 tablespoon of fresh lemon juice, and 1 teaspoon of ground cinnamon. Cook for about 10 minutes until apples are tender. Combine 2 teaspoons of cornstarch with 1 tablespoon of water, then stir into the apple mixture; continue cooking until thickened and cool completely.

Once the cheesecake filling is set, spoon cooled apple compote over the cheesecake layer and drizzle with remaining caramel sauce. Slice and serve to guests.