Preheat oven to 350°F (175°C) and lightly grease a 6-cavity donut pan with non-stick spray.

In a medium mixing bowl, whisk together the flour, sugar, baking powder, and salt.

In a separate small bowl, whisk together the 1/2 cup milk, egg, melted butter, and 1 teaspoon vanilla extract.

Pour the wet ingredients into the dry ingredients and stir until just combined, ensuring no large flour pockets remain.

Transfer the batter to a piping bag or a large plastic bag with the corner snipped off and pipe into the donut pan, filling each cavity about 3/4 full.

Bake for 8 to 10 minutes until the donuts are firm and a toothpick inserted comes out clean.

Allow donuts to cool in the pan for 5 minutes before transferring to a wire rack to cool completely.

Whisk the powdered sugar, cocoa powder, 3 tablespoons milk, and 1/2 teaspoon vanilla extract in a shallow bowl until the glaze is smooth.

Dip the top of each cooled donut into the glaze and place back on the wire rack for the coating to set.