Preheat your oven to 350°F (175°C). Grease a donut pan.
In a large bowl, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, and salt.
In another bowl, mix the milk, eggs, vegetable oil, and vanilla extract.
Combine the wet ingredients with the dry ingredients and mix until smooth.
Fill the donut pan with the batter, about ¾ full.
Bake for 12-15 minutes, or until a toothpick comes out clean. Let them cool in the pan for a few minutes, then transfer to a wire rack to cool completely.
For the frosting, whisk together powdered sugar, cocoa powder, milk, and vanilla extract until smooth. Dip the cooled donuts into the frosting.