Preheat the oven to 180°c / gas 4. Grease a 8 x 12in baking tin and set aside.
Beat together the cream cheese, 1 egg, vanilla extract and 2 tbsp of the sugar and set aside.
Melt the chocolate in a bowl over a saucepan of simmering water. Meanwhile, put the butter in a mixing bowl. Sift in the flour and cocoa powder. Add the remaining eggs and sugar and beat until smooth. Stir the chocolate into the mixture.
Spoon the brownie mixture into a prepared baking tin and level the top with the back of a spoon.
Drizzle the cream cheese mixture over the top and swirl it with a blunt ended knife throughout the tin.
Bake in the oven for 30-35mins or until the brownie springs back when lightly pressed in the middle.
Turn the brownie out onto a wire rack and leave to cool.
Cut into square and serve with a dollop of ice cream.