Preheat oven to 350°F/180°C. Line the base and sides of an 8×8-inch baking pan with parchment paper, leaving enough overhang on the sides for lifting the blondies out after baking.
Put the white chocolate, minus 1-2 tablespoons that you’ll reserve for topping, in a medium heat-proof bowl. Place bowl over a saucepan of simmering water and stir occasionally until the chocolate has melted. You can also melt the chocolate in the microwave by heating it in 30 second increments, mixing chocolate between each and being careful not to overheat and burn it.
Temper the slightly cooled brown butter into the melted chocolate by whisking the white chocolate constantly and slowly pouring the brown butter into it until combined.
Pour batter into prepared pan and smooth the top. Sprinkle the leftover white chocolate over the top. Bake for 20-25 minutes (mine baked closer to 20) until the top is golden and a toothpick inserted into the center comes out with a few moist crumbs. Avoid overbaking, which will make the blondies dry. Let blondies cool completely on a wire rack, then lift them out of the pan and cut into squares (or refrigerate until completely set for perfect cutting).
Blondies can be kept at room temperature or in the refrigerator in an airtight container for up to 3 days. Alternatively, they can be frozen for up to 2 months, then thawed overnight in the fridge.