Pre-heat your oven to 200C/180C Fan/Gas Mark 6. Line an 8" Square Pan with greaseproof paper.
In a small bowl, break up the dark chocolate and melt in the microwave in 20 second intervals, stirring in between to make sure it doesn't burn.
In a large mixing bowl, whisk together melted butter and both sugars. With an electric/stand mixer, go for a solid 3-5minutes so it is totally combined. Add in the eggs and vanilla extract and combine again.
Now, add the melted dark chocolate slowly (check it first, to make sure it isn't so hot that it will cook the eggs) and combine once again.
Add the flour and cocoa powder, then the coconut. Fold gently into the wet mixture with a rubber spatula or wooden spoon until just combined.
Pour the batter into the lined pan and bake for 30 minutes. Let cool on a wire rack before making the frosting.
Add the butter and the coconut rum/milk to a large mixing bowl. Beat with a whisk on high for a minute to soften/combine everything.
Add half the icing sugar, whisk on high. Then add the remaining half and whisk everything on high until fluffy. Add icing sugar as required to meet your desired consistency. Spread over the cooled brownies, top with more coconut, slice and serve!