Melt butter: In a small saucepan over medium heat, melt the butter, watching for it to bubble and the milk solids to darken to a brown hue, releasing a nutty aroma. Take off the heat once it reaches a brown hue. Set the butter aside to let it cool down.
Mix dry ingredients (except the white chocolate): While the butter is cooling down, whisk dry ingredients altogether: flour, baking powder, baking soda, matcha powder and salt in another bowl. Set aside.
Mix wet ingredients: Add the granulated sugar and the brown sugar to the bowl with the browned butter. Whisk until well blended. Add the egg and vanilla extract, continuing to whisk until the mixture becomes smooth and creamy.
Combine the wet and dry ingredients: Add the flour mixture to the butter mixture and fold together with a spatula until some flour patches remain.
Incorporate the white chocolate: Fold half of the small chunks of white chocolate into the dough until evenly distributed.
Chill the dough (covered) for 30 mins to 1 hour in the fridge.
Prep the dough balls: Preheat the oven at 350℉ and while waiting, shape the dough into small balls (with an ice cream scoop) and place them on a baking sheet. Make sure to leave at least 2 inches between the dough balls, as they will expand during the baking processs.
Bake: Bake for 10-12 minutes at 350℉, or until the edges lightly brown. Immediately after taking out the cookies from the oven, gently press the remaining chocolate chunks into the cookies.
Serve: Let the cookies cool down for 15 mins before serving.