Fit a large stand mixer with a paddle attachment, then beat the butter, granulated sugar, and brown sugar until creamy. Place the cracked egg and vanilla extract in the bowl and mix until combined.
Whisk together the all-purpose flour, dry quick oats, cinnamon, and nutmeg in a separate bowl. Add the dry ingredients to the stand mixer and mix until well combined.
Line the air fyre basket wtih cookie parchment paper, add 6-8 cookie dough balls on top, and use your hands to flatten the top of the cookie dough.
Tip: Since you must cook these cookies in batches, place the dough in the refrigerator between batches. The cold cookie dough cooks better in an air fryer than room temperature dough.
Set the air fryer cooking temperature to 320 degrees F, and set the cooking time for 4-6 minutes. Then, allow the cookies to cool in the air fryer basket for at least 5 minutes before transferring them to a cooling rack.
While the cookies cool, make the icing. Using a spoon or a whisk, beat the powdered sugar, milk, and vanilla together in a small bowl.
Dip the tops of the cookies into the icing, allowing the excess icing to drip back into the bowl. Then sprinkle the cookies with a small pinch of cinnamon and quick oats. Let the cookies harden and set for at least 5 minutes before serving.