In a mixing bowl, whisk together flour, cocoa powder, sugar, baking powder, and salt.
In another bowl, whisk together milk, egg, and vanilla extract.
Combine wet and dry ingredients until smooth.
Heat oil in a deep fryer or large pot to 350°F (175°C).
Drop spoonfuls of batter into hot oil and fry until golden brown, about 2-3 minutes.
Remove donut holes with a slotted spoon and drain on a cooling rack.
For the glaze, whisk together powdered sugar, milk, and vanilla extract until smooth.
Dip warm donut holes into the glaze and place back on the rack to set.