Pre-heat oven to 170°C (340°F). Line a 23cm (9-inch) square baking pan with parchment paper. Leave an overhang on the sides so that it is easy to lift the blondies out after they are baked.
In a small saucepan over medium heat, melt your butter. Continue to cook until the butter is golden brown and has a nutty fragrance. This takes about 4-5 minutes. Note that the butter turns very quickly from golden to burnt, so keep an eye on it. Remove from the heat, pour into a large mixing bowl, and leave at room temperature cool.
Into the bowl with the cooled brown butter, add brown sugar and vanilla extract and mix with a rubber spatular until combined. Add the eggs and mix in well.
Sift into this mixture the flour, baking powder, baking soda, and salt and fold through until a few flour streaks remain.
Fold in the white chocolate chips. The batter will be super thick. Spoon batter into the prepared baking tray and level with an offset spatula.
Bake for 20-25 minutes or until lightly browned on top and the sides are set, and a toothpick inserted into the centre comes out with a few moist crumbs. Remove from the oven and let sit in the pan for ten minutes. Using the paper, lift the blondie square out onto a wire rack and leave to cool. In a small bowl, mix powdered icing sugar and 1 teaspoon of water and drizzle over cooled blondies (this step is optional). Cut into 16 squares.