Preheat your oven to 160℃ (140℃ if you're using a fan oven). Line an 8x8-inch tin with baking paper.
Break the white chocolate into pieces and put it in a heatproof bowl with the butter. Melt them together in the microwave, stirring every 20 seconds to prevent seizing or burning. Leave 5-10 minutes to cool.
Use an electric whisk to whisk together the sugar, eggs and vanilla extract in a large bowl, until the mixture becomes pale and increases in volume.
Add the melted white chocolate/butter mixture to the bowl and gently fold it into the whisked eggs/sugar mixture. Then add all of the flour and the matcha powder.
Fold the white chocolate chips into the brownie batter then transfer it to your lined tin.
Bake for around 40 minutes, until the brownies have risen and are beginning to pull away from the tin slightly. There should be a slight wobble in the middle.
Leave in the tin to cool completely then put them in the fridge for 3-4 hours to set. This will make the gooey centre turn firm and fudgy.
Once set, cut into squares and enjoy!