Preheat the oven to 350ºF, and line an 8×8-inch baking dish with parchment paper. Spray with nonstick cooking spray; set aside.
In a medium saucepan, melt the butter over medium-low heat. As the butter melts, it’ll start to foam, then turn a clear golden color. Continue to stir the butter, scraping up any browned specks from the bottom of the pan as it starts to brown. It should have a nutty aroma. Once browned and nutty, turn off the heat and allow to cool for 5 minutes.
Whisk in the brown sugar, egg, and vanilla until smooth. Switch to a wooden spoon, add the flour, baking powder, and salt and stir until just combined. Halfway through mixing in the dry ingredients, add the white chocolate chips and walnuts, and continue mixing until just combined.
Turn batter out into prepared pan, spreading batter evenly with a rubber spatula. Bake for about 20-25 minutes, or until edges are firm and golden and the center jiggles slightly; do not overbake. Blondies firm up as they cool.