Start by proofing the yeast. Add warm water, yeast, and 1 teaspoon of sugar to a small bowl. Let it sit on the counter until the yeast is super bubbly and the mixture has doubled in size.
Mix together milk, sugar, salt, egg, and shortening. Add yeast to the mixture. In a stand mixer with a dough hook attachment, add flour in one cup at a time while mixing. Mix until the dough no longer sticks to the sides of the bowl and is smooth to the touch.
Place the dough in a lightly greased bowl. Cover tightly with plastic wrap and allow to rise until it has about doubled in size, about one hour. You'll know it is ready if you poke the dough and it doesn't bounce back.
Roll the dough out on a floured surface until about ½ inch thick. Cut out the donut shapes and place them on a baking sheet lined with parchment paper. Cover with a thin kitchen towel and let rise for 30 minutes.
Preheat the Air Fryer to 350 degrees. Generously spray a cooking spray like Pam or coconut oil spray in the basket. Carefully place donut dough in the Air Fryer basket. Only put as many donuts in as will fit without touching each other. Spray the tops of the donuts with cooking spray. Air fry for 5 minutes.
To make the chocolate icing, combine powdered sugar, cocoa powder, and milk in a bowl wide enough to fit the top of a donut. Mix with a fork until a smooth glaze forms.
Take the donuts out of the Air Fryer and place them on a wire rack with a parchment paper-lined baking sheet underneath. When cool enough to touch, dip the top of the donuts in the chocolate glaze. Place back on the wire rack and top with sprinkles. Donuts are best served immediately.