Preheat oven to 350°.
Prepare a 9 x 9-inch square baking pan by spraying with oil and lining with parchment paper. Allow the parchment to hang over 2 of the sides to act as "handles" for lifting out the cake later.
In a stand mixer bowl, whisk together the eggs, sugar, and vanilla extract until pale yellow and fluffy.
In a separate bowl, combine the flour, cocoa powder, baking powder, and sea salt. Sift these dry ingredients over the egg mixture.
Whisk together all of the ingredients on low speed until combined. Gradually mix in the milk, followed by the melted and cooled butter.
Pour the batter into the prepared pan and smooth the top. Bake for 25-30 minutes until the cake springs back when touched and a tester comes out clean. Do not overbake.
Let the cake cool for 30 minutes in the pan on a cooling rack. Gently lift the cake out of the pan using the parchment as handles.
Prick the cake all over with a fork or tip of a knife.
Pour the glaze over the top of the cake, allowing it to soak into the holes.
Sprinkle the top of the cake with coconut and cool completely.
Cut the cake into 16 squares with a serrated knife. Serve immediately or store in an airtight container.