In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, baking soda, salt, and nutmeg until well combined.
In another bowl, mix the buttermilk, egg, melted butter, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix; it's okay if the batter is a bit lumpy.
Place the dough onto a floured surface and gently roll it out to about ½-inch thick.
Use a biscuit cutter to cut out donut shapes. If you have a smaller cutter, use it to cut out the centers of the donuts.
Preheat the air fryer to 350°F (175°C) for about 5 minutes.
Line the air fryer basket with parchment paper (if desired) and place the donuts inside, leaving space between them.
Air fry the donuts at 350°F (175°C) for 8 minutes, flipping halfway through, until golden brown and cooked through.
While the donuts are cooling, prepare the glaze by mixing powdered sugar with milk until you reach your desired consistency.
Dip the cooled donuts into the glaze and place them on a cooling rack to let the glaze set.