Preheat the oven to 170°C (340°F).
Sift the matcha powder and flour together.
Cream the butter and sugar in a bowl until smooth.
Add eggs one at a time, mixing well after each addition.
Add the sifted matcha-flour mixture and mix until combined.
Add chopped white chocolate and mix evenly.
Pour the batter into a pan and spread it evenly.
Bake in the oven for 20 minutes.
Let cool, then cut into bite-sized pieces.