Preheat the oven to 350°F. Cut the butter into several tablespoon-sized chunks and add it to a small light-colored skillet. Heat the butter over medium heat, stirring constantly, until the butter solids turn deep brown and develop a nutty aroma (it will first become foamy, then the solids will sink to the bottom and turn brown).
While the butter is browning, add the brown sugar and granulated white sugar to a large mixing bowl.
Once the butter has browned, remove it from the heat immediately to prevent burning, and carefully pour it into the mixing bowl with the sugars. Whisk the brown butter and both sugars together until smooth.
Add the eggs and vanilla extract to the bowl and whisk until smooth.
In a separate bowl, stir together the all-purpose flour, baking powder, and salt until well combined. Add the flour mixture to the bowl with the wet ingredients. Use a rubber spatula to stir the flour into the batter until evenly combined.
Finally add the white chocolate chips to the batter and fold them in until just combined.
Line an 8x8 baking dish with parchment paper. Add the blondie batter to the baking dish and spread it out evenly. Feel free to add a few more white chocolate chips on top of the batter.
Bake the blondies in the preheated oven for 35 minutes or until a toothpick inserted comes out clean.
Remove the blondies from the oven and let them cool for 10-15 minutes before lifting the parchment paper out of the baking dish. Slice into 12 bars and serve.