Preheat the oven to 180°C, fan 160°C, gas mark 4. Line a 20 x 25cm cake tin with baking parchment.
Melt the butter, plain and milk chocolate together in a large bowl, then allow to cool slightly.
In a separate bowl, beat together the eggs, caster sugar and vanilla. Whisk in the cooled chocolate mixture, then fold in the flour and chopped white chocolate.
Transfer the mixture to the prepared tin and bake in the preheated oven for about 45 minutes until the top is crisp and pale and the centre is almost set. Allow to cool in the tin, then cut into 20 squares.