Preheat the oven to 350°F and line an 8x8″ baking pan with parchment paper. Set aside.
In a large bowl, whisk together the melted butter and brown sugar. Then add in the egg, egg yolk, and vanilla extract. Mix well to combine.
In a separate mixing bowl, add the flour, baking powder, and salt. Sift the matcha powder through a fine mesh strainer to remove any clumps, then whisk the mixture to combine.
Pour the wet ingredients into the dry ingredients. Mix until just combined. Fold in the white chocolate chips but do not over mix!
Pour the matcha batter into the prepared pan, spreading it into an even layer.
Bake for 25-30 minutes (check after 25 minutes). The edges should be golden brown, the middle puffed up and a toothpick inserted into the middle comes out with a few wet crumbs (slightly undercooked, but not wet batter). It'll continue to cook as it cools.
Once cool, use a sharp knife to cut the matcha white chocolate brownies into squares and enjoy!