Preparation

1. In a small bowl, dissolve the yeast and ½ teaspoon sugar in the warm milk. Let stand 5 to 10 minutes, or until mixture is foamy.
2. Put ¾ cup of the flour, the remaining sugar, salt, cinnamon, and nutmeg into a large mixing bowl. Whisk to combine. Once yeast has proofed, add it to the flour/sugar. Using a wooden spoon, stir to combine.
3. Whisk the egg, buttermilk and vanilla extract together and then slowly mix into the flour mixture. Lightly dust a clean work surface with flour and transfer dough to the surface, dusting lightly with flour. Using your hands to knead, add additional flour as necessary, 1 teaspoon at a time, to keep dough from sticking to your hands.
4. Add the butter, 1 piece at a time, until all has been mixed into the dough. Again, continue adding flour, 1 teaspoon at a time, to keep dough from sticking to your hands. The dough should be tender and smooth, and when pulled should not break apart.
5. Form dough into a ball and put in a clean mixing bowl, cover with plastic wrap and allow to rest for 1 hour. After 1 hour, gently turn dough over and press dough down (do not punch). Cover and allow to rest for another hour.
6. Place the Air Fryer Basket into the Baking Pan. Lightly coat with nonstick cooking spray. Line a separate baking sheet with parchment paper. Divide the dough into 16 pieces.
7. Working with one piece at a time (keeping the others covered loosely with plastic wrap), form into a small ball and roll between hands to ensure that it is smooth. Put round on the lined baking sheet and cover loosely with plastic wrap. Repeat with the remaining pieces of dough.
8. Once 8 doughnuts have been formed, transfer them to the Air Fryer Basket and put into the oven in Rack Position 2. Set to Air Fry at 350°F for 5 minutes. Air fry until doughnuts just get a bit of color at the edges. Repeat with remaining doughnuts.
9. While doughnuts are air frying, melt additional butter in a small saucepan set over low heat. Put cinnamon sugar in a shallow bowl. Reserve.
10. Remove doughnuts from oven and immediately brush with butter on all sides and then gently toss in cinnamon sugar. Serve immediately.