Preheat the oven to 180°C/gas mark 4. Place 100g of the white chocolate and the butter in a heatproof bowl over a pan of simmering water and heat until melted.
Meanwhile, grease and line a 20 x 20cm baking dish with greaseproof paper. Combine the melted butter and white chocolate with the sugar, then gradually stir through the beaten eggs. Fold through the flour and matcha powder then stir through the remaining 100g of white chocolate. Pour this mixture into the lined tin and bake for 30-35 minutes or until a skewer inserted in the middle comes out clean.