Preheat oven to 350F. Melt butter in the microwave. Once fully melted, add the white chocolate chips. Whisk until melted, then whisk in matcha.
Combine eggs, sugar and vanilla in a large mixing bowl. Beat on high with an electric hand mixer until thick and creamy. Whisk in the matcha mixture, then fold in the flour.
Scrape the batter into an 8×8 baking pan lined with parchment. Bake 25-30 min.
Allow to cool in the pan before slicing and serving.