Stir lukewarm milk with 1 teaspoon sugar and yeast, then let it stand for 5-10 minutes until foamy.
Mix in remaining sugar, salt, egg, melted butter, and flour until a soft dough forms.
Knead the dough for 5-7 minutes until smooth, elastic, and slightly tacky.
Place the dough in a greased bowl, cover, and let rise for about 1 hour or until doubled.
Roll the dough about 1/2 inch thick, cut into donut shapes, and let rise again for 20-30 minutes.
Preheat the air fryer to 350°F for 2-3 minutes and lightly spray the basket and donut tops.
Air fry donuts in a single layer for 5-6 minutes, flipping halfway, until puffed and lightly golden.
Whisk melted butter, powdered sugar, vanilla, and hot water into a smooth glaze, then dip warm donuts and set on a rack.