Preheat oven to 325 degrees. Line a 12-cup muffin pan with paper liners, or use a silicone muffin pan for stick free, no liner cheesecakes.
In a medium bowl, combine the graham cracker crumbs, sugar, cinnamon, and melted butter. Stir together until combined. Add a heaping tablespoon into each muffin, and press down evenly. Set aside.
In a medium bowl, add peeled, chopped apples and lemon juice. Stir to coat. Stir in brown sugar, cinnamon, nutmeg, and corn starch, set aside.
In a large bowl, beat the room temperature cream cheese with a hand mixer or stand mixer until smooth, beat in sugar, eggs, vanilla, and flour until creamy and smooth. Divide evenly into the muffin pan over the crusts. Spread into even layers. Top each cheesecake with apple mixture. Press down gently. Bake for 35 minutes.
While the cheesecakes are baking, prepare the caramel sauce. In a medium saucepan combine brown sugar, heavy cream, and butter over medium-low heat. Whisk for about 5-6 minutes. Mixture will be bubbly, but should not be burning or smoking. Whisk in the vanilla and pinch of salt. Whisk for 1 minute. Remove from heat. Sauce will thicken as it cools.
Once cheesecakes have cooled slightly, drizzle generously with caramel sauce. Refrigerate and chill for at least 3 hours.