Preheat oven to 325°F (163°C) and line an 8x8-inch pan with parchment paper.
Whisk together flour, matcha powder, baking powder, and salt in a bowl.
Melt butter and white chocolate together until smooth.
In another bowl, whisk sugar, eggs, and vanilla until combined.
Stir the melted chocolate mixture into the egg mixture.
Gradually fold in the dry ingredients until just combined.
Pour batter into the pan and bake for 25 minutes or until a toothpick comes out clean.
Let brownies cool in the pan for 10 minutes, then transfer to a rack.