Froth up the yeast by combining warm water, warm milk (108°F), dry active yeast, and 1 tablespoon granulated sugar. Let it sit for 5 minutes until frothy.
In a stand mixer, combine 1/3 cup granulated sugar, melted butter, egg, egg yolk, vanilla extract, flour, salt, and the yeast mixture. Mix on low until combined, then beat on high for 5 minutes, adding flour a tablespoon at a time if dough is too sticky.
Place dough in a greased bowl, cover with towel or plastic wrap, and let rise for 1 hour until doubled.
Punch down the risen dough and transfer to a floured surface.
Roll dough to 1/2 inch thickness and cut donuts using a donut cutter or two biscuit cutters.
Place cut donuts on parchment-lined baking sheet, cover lightly, and let rise again for 20-30 minutes.
Preheat air fryer to 345°F and spray basket with cooking spray.
Spray donuts with cooking spray and place in air fryer basket without touching. Air fry for 4 minutes.
Repeat air frying with remaining donuts. Transfer fried donuts to plate lined with paper towels.
To make glaze, whisk powdered sugar, milk, light corn syrup, and vanilla extract until smooth.
While donuts are warm, dip them in the glaze and place on cooling rack to set.
