Preheat the oven to 180°C (350°F) and line a 9"x9" baking tin with baking paper.
Melt the butter and dark chocolate together.
Dissolve the espresso powder and water together.
Mix the eggs, sugar, brown sugar, vanilla extract and espresso together until the mixture becomes a light golden colour.
Mix in the chocolate mixture.
Stir in the flour and cocoa until just combined.
Mix in the chocolate chips.
Pour the brownie mixture and bake for 20-25 minutes. The top and sides will be set and the middle will have crumbs attached to a skewer inserted but should not be wet.
Allow to cool to room temperature before topping with the buttercream.
Espresso Buttercream;
Dissolve the espresso in the water.
Beat the butter, cocoa and coffee mixture together.
With the beaters on, add the icing sugar slowly until it is all combined.
If the mixture is too tough, add a little of the milk.