Step 1: Preheat your oven to 350°F (175°C) and grease an 8x8 inch square baking pan, lining it with parchment paper for easy removal.
Step 2: In a large microwave-safe bowl, melt the butter and 1 cup of the white chocolate chips together in 30-second intervals, stirring until smooth.
Step 3: Whisk the granulated sugar into the butter and chocolate mixture vigorously for about 2 minutes until well combined and slightly shiny.
Step 4: Add the eggs one at a time, whisking thoroughly after each addition, then stir in the vanilla extract.
Step 5: In a separate bowl, sift together the all-purpose flour, matcha powder, and salt to remove any lumps.
Step 6: Gently fold the dry ingredients into the wet ingredients using a spatula until just combined. Do not overmix.
Step 7: Fold in the remaining 1/4 cup of white chocolate chips if desired, then pour the batter into the prepared pan.
Step 8: Bake for 25-30 minutes. The edges should be firm, but a toothpick inserted into the center should come out with a few moist crumbs.
Step 9: Allow the brownies to cool completely in the pan before slicing into 16 squares.