Preheat your oven to 350°F (175°C) and prepare a baking dish.
In a mixing bowl, whisk together the flour, cocoa powder, baking powder, and salt.
Melt the butter in a small saucepan over low heat, then remove from the heat and stir in sugar until well-combined.
Add eggs, matcha powder, and vanilla extract to the butter and sugar mixture, whisking until smooth.
Gradually stir the dry ingredients into the wet mixture until just combined, then fold in the white chocolate chips.
Pour the batter into the prepared baking dish, spreading it evenly with a spatula.
Bake for 25-30 minutes, or until a toothpick inserted comes out with a few moist crumbs.
Once baked, let the brownies cool in the pan for about 10 minutes before transferring to a wire rack.
Cut into squares and serve, optionally dusting with additional matcha powder for presentation.