NOTE: you can make apple pie filling ahead of time or while cheesecake is baking.(If you choose to make it ahead, store it in the refrigerator, in a food storage container with a lid. Warm it up before adding to the cheesecakes.)
Peel, core, and dice the apples.
In a medium pot, over medium heat, melt butter and add diced apples. Stir well.
Stir in brown sugar, apple pie spice, and vanilla extract and cover with a lid. Cook for a few minutes, stirring occasionally, until the apples start to soften. Take off the lid.
Cook uncovered, until apples are soft and juices are cooked down about half way. Stir occasionally. (This will take about 15 minutes.)
Sprinkle flour over apples and stir well. Cover and cook for a few minutes.
Take off heat and set aside until ready to use. (Or cool and refrigerate in a contained with a lid.)
Combine graham crackers and apple pie spice in a small mixing bowl. Mix in melted butter until completely incorporated.
Line a muffin pan with cupcake liners.
Add about 1 1/2 to 2 tbsp of graham cracker mixture into each cup. Use the back of the tablespoon to press the cracker mixture all over the bottom and a little up the sides.
Beat cream cheese and sugar for a couple of minutes with an electric mixer on medium speed.
Add egg and sour cream while still beating.
Lower the speed and beat in heavy whipping cream, cornstarch, and apple pie spice.
Scrape sides and bottom of the bowl and beat the mixture for a few more seconds until completely smooth and all blended.
Use an ice cream spoon to scoop even amounts of filling into each cup, filling them 3/4 of the way full.
Preheat the oven to 325°.
Bake the cheesecakes for 18-20 minutes. (The centers will still giggle slightly, so don't think it's undercooked.)
Take the cheesecakes out of the oven and let them cool to room temperature before adding the topping.
Generously top each cheesecake with the prepared apple pie topping.
Cover the pan with plastic wrap or aluminum foil and chill for at least 4 hours.
Optional: Drizzle each cheesecake with caramel sauce before serving.