Mix Dry Ingredients: In a large bowl, whisk together 150g glutinous rice flour, 30g cornstarch, 30g fine sugar, and 6g matcha powder until well combined and free of lumps.
Add Wet Ingredients: Gradually pour 220g of whole milk into the dry ingredients while stirring continuously until you have a completely smooth, lump-free batter.
Cook the Dough: Pour the mixture into a non-stick skillet. Add 20g of softened butter. Cook over low-medium heat, stirring constantly with a silicone spatula. The mixture will thicken and eventually form a smooth dough ball that pulls away from the sides of the pan (about 3-4 minutes).
Knead the Dough: Transfer the dough to a clean surface. Let it cool for 5 minutes until safe to handle. Then, knead for about 2 minutes by stretching, folding, and pressing until it becomes smooth and very elastic.
Chill to Set: Press the dough into a square container lined with plastic wrap, creating an even layer about 2-3cm thick. Refrigerate for 30 minutes until firm.
Cut and Serve: Remove the set dough from the container. Dust the top with the reserved 2g of matcha powder (and powdered sugar if using). Use a sharp knife to cut into small squares. Serve immediately or chill for later.