Grease and line a 9" (23cm) springform pan.
Pre-heat the oven to 175°C (350℉).
Add the butter and both chocolates to a pan and gently heat until everything has just melted.
Add the brewed coffee, stir, and set to one side.
In a large bowl, whisk the eggs and sugars together.
Pour in the melted chocolate/butter mixture and whisk quickly (just until combined).
Sift the flour and cocoa together, and stir into the wet ingredients (again, just until everything has come together - don't over-mix).
Pour into the prepared pan and bake for around 25 minutes.
When ready, the tops of the brownie will feel very firm but an inserted skewer will not be completely clean.
When ready, remove from the oven. Wait ten minutes and then remove the springform sides, then allow to cool completely (you may also find an hour or two in the fridge will make it easier to slice).