Sift cake flour, green tea powder, baking powder, sugar, and salt together. Add diced butter and cut it into the mixture using a scraper.

Coat the butter with flour and cut until the mixture resembles coarse crumbs.

Mix egg and milk together, then add to the dry mixture. Use a spatula to mix by cutting through the dough.

When the dough is almost combined, add white chocolate chips and mix gently. Wrap the dough in plastic wrap and refrigerate for at least 1 hour.

Roll out the dough and perform a three-fold technique three times. Work quickly while keeping the dough cold.

Cut the dough into desired shapes.