In a large bowl, using an electric mixer fitted with a hook attachment, add the flour, sugar, salt, milk, egg yolk, and yeast and knead on low speed until it comes together about 3-4 minutes. Scrape down the sides of the bowl halfway through. Let rest for 20-30 minutes.
Then knead on high speed for about 6-8 minutes until the dough releases from the sides of the bowl and passes the windowpane test.* Reduce the speed to medium-low and gradually add the butter and knead until the butter is fully incorporated. Once all of the butter has been added, increase the speed to high and knead until the dough is smooth and releases from the sides of the bowl. It's a soft, smooth dough, that is slightly sticky.
Lightly spray a medium-sized bowl with nonstick spray or oil and transfer the dough to the bowl; lightly oil the top of the dough as well. Cover and let rest in a warm spot (68-75°F / 20-24°C) for 1 hour. Then transfer the dough to the refrigerator and chill for 1-2 hours until doubled in size.
Lightly spray a 9x13-inch (23x33cm) sheet with nonstick spray or oil and set aside.
On a very lightly floured surface (use as little flour as possible - just enough so that the dough doesn't stick to the rolling pin and surface), flatten and shape the dough into a square with your hands and roll it out until it is between ¼-1/2 inch (0.6-1.3 cm) thick. Using a very lightly floured donut cutter, cut out 3-inch (7.5-cm) donuts. Place the rings and holes about 2 inches (5 cm) apart on the prepared sheet. Reroll and cut until you run out of dough.
Lightly spray a piece of plastic foil with nonstick spray and cover the donuts. The non-stick spray ensures that the dough does not stick to the plastic foil after it has risen. Let rise in the refrigerator overnight.
Take the donuts out of the fridge and let sit on the kitchen counter for 10 minutes. In the meantime, preheat the air fryer to 375°F (190°C) for 5-10 minutes.
Lightly spray the air fryer basket with oil or nonstick spray and place 3-4 donut rings (depending on the size of your air fryer basket) in the air fryer basket and bake for 2-3 minutes on each side until golden brown. Bake the holes for 1-2 minutes on each side. While the donuts are baking, prepare the glaze.
In a medium bowl, whisk the powdered sugar, butter, and vanilla until combined. Then add the hot water and whisk until smooth. Dip the warm rings on both sides in the glaze and allow to drip off. Then glaze the holes with the remaining glaze. Transfer to a wire rack, allow the glaze to set and harden for about 15-30 minutes and serve. They are best eaten fresh on the same day but you can store them in a container at room temperature for up to 2 days.