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, one at a time and mixing in between. Add the vanilla and mix again.
Now, add the 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, fold gently into the wet mixture with a rubber spatula or wooden spoon until just combined. Fold in the chopped chocolate.
Pour the batter into the lined pan and bake approx 25-30 minutes. Remove pan from oven once cooked, and leave the brownies in the pan on a wire rack until totally cooled. Then remove and slice!