Preheat oven to 200°C (390°F) top and bottom heat and line a rectangular cake pan (ca 20x30 cm, 8x12 in) with baking paper.
Melt butter in a bowl and add milk. Set aside.
In another mixing bowl, use an electric mixer to whisk the egg and sugar until light and fluffy.
Combine the dry ingredients and sift into the egg mixture. Add the milk and butter mixture and stir until you have a smooth batter.
Pour batter into the cake pan and bake for about 20 minutes, until a toothpick comes out clean.
Glaze
Melt the butter in a saucepan over medium heat. Add the coffee, cocoa powder, vanilla, and powdered sugar. Stir until smooth and remove from heat.
Decoration
Once the cake has cooled, pour the glaze over the top of the cake. Sprinkle the top with shredded coconut. Wait until the glaze sets before removing the cake from the pan.