Preheat your oven to 350°F (175°C). Lightly grease and flour a 12-cavity donut pan, tapping out any excess flour. Set aside.

In a large mixing bowl, whisk together the all-purpose flour, unsweetened cocoa powder, granulated sugar, baking powder, baking soda, and salt until well combined.

In a separate medium mixing bowl, whisk together the egg, milk, melted butter, and vanilla extract until smooth.

Pour the wet ingredients into the dry ingredients. Stir with a rubber spatula until just combined. Be careful not to overmix; a few lumps are fine.

Transfer the batter to a piping bag (or a large Ziploc bag with a corner snipped off) for easier filling. Pipe the batter evenly into the prepared donut cavities, filling each about two-thirds full.

Bake for 10-12 minutes, or until a toothpick inserted into a donut comes out clean and the donuts spring back when lightly touched.

Let the donuts cool in the pan for 5 minutes before carefully transferring them to a wire rack to cool completely. Do not glaze warm donuts.

In a medium bowl, whisk together the sifted powdered sugar, sifted cocoa powder, 3 tablespoons of milk, vanilla extract, and a pinch of salt until smooth and lump-free. Add an additional tablespoon of milk if the glaze is too thick, or a teaspoon more powdered sugar if it's too thin, until you reach a pourable but not watery consistency.

Once the donuts are completely cool, dip the top of each donut into the chocolate glaze, allowing any excess to drip off. You can also use a spoon to coat them.

Place the glazed donuts back on the wire rack set over a piece of parchment paper or foil to catch drips. Allow the glaze to set for about 15-20 minutes before serving.