Makes 1 dozen donuts plus donut holes
1 cup milk, lukewarm (about 100 degrees F)
1 packet active dry yeast
1/4 cup + 1 teaspoon granulated sugar
1/2 teaspoon kosher salt
1 egg, room temperature
1/4 cup unsalted butter, melted
3 cups all-purpose flour
Cooking spray
3 tablespoons unsalted butter
1 cup powdered sugar
1 teaspoon vanilla extract
2 tablespoons hot water, or as needed
1. In the bowl of a stand mixer fitted with dough hook, gently stir yeast with 1 teaspoon sugar and lukewarm milk. Set aside for 10-15 minutes, until foamy.
2. Add remaining sugar, egg, melted butter, salt, and 2 cups flour to milk mixture. Mix on low speed until combined, then add remaining cup of flour. Increase speed to medium-low and kneed for 5 minutes, until dough is elastic and smooth. Place the dough into a greased bowl and cover it with plastic wrap. Allow to rise for at least 1 hour, until doubled.
3. Turn dough onto a floured surface and gently roll to about a 1/2-inch thickness. Cut out 12 donuts with a donut cutter (or a 3-inch round cutter with a 1-inch round cutter to remove centers).
4. Transfer donuts and donut holes to a parchment paper-lined baking sheet and cover loosely with greased plastic wrap. Allow donuts to rise further, about 30-45 minutes.
5. Spray air fryer with spray and carefully transfer two tester donuts to basket. Spray tops of donuts and cook at 330-340 degrees for 4 minutes. Check after 2 minutes on the first batch to assess temperature! Continue with remaining donuts and donut holes.
6. While the donuts are in the air fryer, melt butter in a small saucepan over medium heat. Stir in powdered sugar and vanilla until smooth. Remove from heat and stir one tablespoon of hot water at a time until glaze is thin. Dip hot donuts and donut holes in glaze, using two spoons to carefully handle. Allow to cool slightly on a wire rack over a rimmed baking sheet to allow excess glaze to drip off. Serve warm!