Preheat the oven to 180C/350F/Gas 4. Grease a 20cm/8in square cake tin with butter.
For the brownies, 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.
Add the chopped white chocolate and macadamia nuts and carefully fold them into the mixture.
Spoon the brownie batter into the prepared cake tin and shake gently until level. Transfer the tin to the oven and bake for 30-35 minutes, or until a skewer inserted into the centre of the brownies comes out clean. Set aside to cool.
Meanwhile, for the frosting, in a mixing bowl, whisk together the butter, icing sugar and vanilla seeds using an electric whisk until smooth and well combined.
Add the peanut butter and whisk until the mixture is smooth and well combined. (Add a little milk, if using, to loosen the mixture, as necessary).
Once the white chocolate brownies have cooled, spread over the peanut butter frosting in an even layer. Cut the brownies into squares, carefully remove them from the tin and serve on a large serving plate.