Preheat the oven to 160°c / gas 3. Grease and line a 20.5cm (8in) shallow square baking tin.
Combine the butter and chocolate in a large heatproof bowl. Place the bowl on top of a saucepan of gently simmering water and melt the butter and chocolate, stirring occasionally.
In a mixing bowl, whisk together the eggs and sugar with an electric whisk until the mixture has doubled in volume and looks pale, usually around 5-8 mins.
Pour the cooled chocolate mixture into the egg and sugar mixture, add the vanilla extract and fold together.
Sift in the flour and cocoa on top of the mixture and fold in gently.
Pour into the tin and bake for 25-30mins until just set on top and a knife comes out a little wet from the middle. Remove from the oven and let the brownie cool in the tin for an hour before turning out onto a chopping board. Cut into 12 square using a sharp knife.