Preheat the oven to 180 C / Gas 4. Grease a 20cm square cake tin with butter.
For the blondie mixture, in a bowl beat together the sugar and eggs until pale and fluffy. Beat in the melted butter a little at a time, making sure each addition of butter is fully incorporated before adding the next. Add the flour and carefully fold it into the mixture using a metal spoon.
For the brownie mixture, break up the dark chocolate. Put into a heatproof bowl and melt gently in a pan over barely simmering water, making sure the water doesn't touch the base of the bowl. Remove the bowl from the heat and leave to cool until needed.
Beat the butter and sugar until fluffy. Gradually beat in the eggs, beating well after each addition. Beat in the vanilla.
Spoon the cooled melted chocolate onto the butter mixture then mix in thoroughly. Sift the flour and cocoa powder onto the mixture and gently stir in.
Pour the brownie mixture into the tin, then top with the blondie mixture. Use a knife to swirl through the mixtures to create a marbled effect.
Bake in the preheated oven for 20 minutes or till set in the centre.