Line a baking tray with non-stick baking paper. Preheat oven to 175°C.
Using an electric beater, beat the butter and brown sugar in a large bowl until thick and creamy. Add egg and vanilla essence and continue to beat until well combined.
Fold in the plain flour and self-raising flour until just combined, then add the white chocolate and macadamias to form a chunky mixture.
Place spoonfuls of the cookie mixture on the prepared tray and gently press down to flatten a little. Bake for 15-20 minutes or until golden brown. Remove from oven and set aside for a few minutes to cool slightly, then transfer to a wire rack to cool completely.