In a medium bowl combine flour, cornstarch and baking powder and whisk.
In a large bowl beat together melted butter and the two kinds of sugar until well combined. Add egg and vanilla and whisk until homogeneous. Gradually add the dry mixture and stir until a soft dough forms. Add the chopped pistachio and white chocolate. Gently mix until absorbed in the batter.
Wrap the dough in cling film and leave it in the fridge for 30 minutes to 1 hour.
Preheat oven to 320° F/ 160° C. Line 2 large baking pans with baking paper or baking mats.
With your hands make balls out of the dough and arrange them on the prepared baking pans. Leave some distance in between as they will grow during baking.
Bake on medium rack for 10 to 15 minutes or until the edges of the cookies start becoming golden brown (watch them carefully). If the bottoms are brown but the tops seem still too white, bake for another 5 minutes on top heat only.
Remove the cookies from the oven and let cool for 5 minutes on the pan, before transferring them to a wire rack.