In a mixing bowl, combine the flour, granulated sugar, baking powder, salt, and nutmeg. Whisk until well mixed.
In a separate bowl, whisk together the milk, egg, vanilla extract, and melted butter.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Lightly flour a surface and roll out the dough to about ½-inch thickness.
Use a donut cutter or two round cookie cutters to cut out your donuts. Gather the scraps and re-roll as needed.
Preheat your air fryer to 350°F (175°C).
Line the air fryer basket with parchment paper if desired. Place the donuts in a single layer in the basket, ensuring they do not touch.
Air fry the donuts at 350°F for about 10-12 minutes, or until they become golden brown. Flip them halfway through for even cooking.
While the donuts are cooking, prepare the glaze by mixing the powdered sugar, milk, and vanilla extract until smooth.
Once the donuts are done, let them cool for a few minutes before dipping them in the glaze.