Preheat oven to 350°F. Line an 8x8 cake pan with parchment paper.
Add the eggs, sugar, and vanilla extract to a large bowl. Use an electric whisk to whip until fluffy.
In another, smaller bowl, whisk together the flour, cocoa, baking powder, and salt. (If cocoa is clumpy, run the whole mixture through a sieve or sifter.)
Stir in the dry mixture, butter, and milk into the whipped egg-sugar mixture. Use the electic whisk on its lowest setting or a spatula to combine until blended.
Pour the batter into the cake pan. Use a spatula to get everything out and to smooth the top. Bake for about 25-35 minutes or until a toothpick comes out clean.
While the cake is cooling, make the glaze. First, melt butter in a saucepan over medium heat. Next, stir in the powdered sugar, cocoa powder, coffee, and vanilla extract. Mix until smooth, adding more coffee as needed to get the right consistency. (Note: if you want a more fluffy, frosting-like mixture, use an electric whisk to combine everything).
Carefully transfer the cake to a cutting board or large plate. Use a toothpick to stick some holes into it. (This is not a must, but allows the glaze to seep into the cake.)
Spread the glaze over the cake using a spatula. Sprinkle with the coconut. Slice into as many pieces as you want and enjoy!
