Bring a medium sized saucepan to a boil.
Meanwhile, prepare the chestnuts by placing them flat side down and rounded side up on a chopping board.
Use a serrated knife to score an X on the round side that is deep enough to penetrate the hard shell but not too deep as to cut the actual chestnut (this is important so that the steam can escape and the chestnuts don't explode as well making peeling much easier).
Add the chestnuts to the boiling water and continue to boil for 5 minutes.
Use a slotted spoon to remove the chestnuts and drain off the excess water.
Preheat the air fryer for 5 minutes.
Place the chestnuts, flat side down with the X facing upwards.
Air fry the chestnuts at 374F/190C for roughly 10 minues (the amount of cooking time will vary depending on the size of the chestnuts). You will know when they are completely cooked because the flesh should be more exposed.
Once cooked, place them in a tea towel while still hot and scoop the chestnuts together in a heap for about one minute (this will help to make steam and make them more manageable to peel).
Peel the chestnuts while they are still hot and don't allow them to get cold or they will be far too difficult to peel.
Once peeled, put them in a medium sized bowl.
Place the cane sugar, nutmeg and cinnamon in a small bowl and set aside.
Combine the melted butter with the vanilla extract in a small bowl.
Drizzle and coat the chestnuts with the butter.
Immediately sprinkle the chestnuts with the sugary mixture.