Preheat your oven to 325F. Line an 8x8 inch baking pan with parchment paper and lightly grease the sides.
In a light-colored saucepan, melt the butter over medium heat. Continue cooking, swirling the pan occasionally, until the butter turns golden brown and smells nutty, about 4 to 5 minutes. Watch carefully to avoid burning. Remove from heat and let it cool for 5 minutes.
Pour the brown butter into a large bowl. Add the brown sugar and whisk until smooth. Add the egg, egg yolk, miso paste, and vanilla extract, then whisk vigorously until the mixture is thick and glossy, about 1 minute.
Add the flour, baking powder, and salt to the bowl. Fold gently with a spatula until just combined with no dry streaks remaining. Fold in the white chocolate chips.
Spread the batter evenly into the prepared pan. Sprinkle a generous pinch of flaky sea salt over the top.
Bake for 22 to 25 minutes, until the edges are set and the center has the slightest jiggle. The blondies will firm up as they cool. Let them cool in the pan for at least 30 minutes before slicing.