Preheat the oven to 350 degrees Fahrenheit.
To brown the butter, melt the butter sticks in a saucepan over medium heat. Stir occasionally until it develops a nutty aroma and browned bits form at the bottom. Once browned, transfer the butter to a mixing bowl.
Add the white sugar, brown sugar, salt, and eggs to the bowl with the browned butter. Whisk until everything is well combined.
Next, add the vanilla extract and whisk again until fully incorporated.
Gently fold in the flour and matcha powder using a rubber spatula, mixing until the batter is smooth and has turned a vibrant matcha green.
Fold in the white chocolate chips and transfer the batter into a prepared baking dish, spreading it evenly. Sprinkle a few extra white chocolate chips on top.
Bake for 25-28 minutes, or until the edges are lightly golden and the top has a crinkled texture.
Remove from the oven and let the brownies cool completely before cutting and serving.
Once cool, cut into slices.