Preheat the oven to 360F. Melt half of the butter with the dark chocolate in a thick-bottomed pan, and melt the white chocolate in another pan with the rest of the butter. Leave to cool.
Using the mixer, beat the eggs briefly with the sugar and vanilla. Divide the flour into 2 portions and add a pinch of salt to each.
Beat half of the egg-sugar mixture through the dark chocolate. Then add in half of the flour and half of the nuts and mix. Do the same with the white chocolate mixture.
Pour the white and brown brownie mixture into two different sides of the cake tin. Use a spatula to partially mix the two colours, creating a swirl. Bake the brownies for about 30 minutes. When ready, the surface should be dry to touch.