Step 1: Preheat your oven to 350°F (175°C) and line an 8x8 inch baking pan with parchment paper, leaving a slight overhang.
Step 2: In a microwave-safe bowl or over a double boiler, melt the butter and chopped white chocolate together until smooth. Let it cool slightly.
Step 3: In a large mixing bowl, whisk the eggs and granulated sugar for about 3-5 minutes until the mixture is pale and thick.
Step 4: Stir the vanilla extract and the melted chocolate-butter mixture into the egg mixture until well combined.
Step 5: Sift the flour, matcha powder, and salt into the wet ingredients. Gently fold with a spatula until just combined. Do not overmix.
Step 6: Fold in the white chocolate chips if using, then pour the batter into the prepared pan and smooth the top.
Step 7: Bake for 22-25 minutes. The edges should be set, but the center should still have a slight jiggle. Do not overbake to ensure they remain fudgy.
Step 8: Allow the brownies to cool completely in the pan before lifting them out and slicing into squares.