In a large mixing bowl, whisk together the glutinous rice flour, cornstarch, matcha powder, and sugar until everything is evenly combined with no lumps. Slowly pour in the milk while whisking continuously until you have a smooth, lump-free batter.

Strain the batter through a fine sieve into a nonstick pan — this ensures a silky, smooth texture and removes any undissolved bits. Add the softened butter, then cook over low heat while stirring constantly with a silicone spatula. The mixture will thicken gradually, then clump into a dough. Continue stirring until the dough no longer sticks to the pan or spatula, about 5–7 minutes. Transfer to a container and let it cool until warm.

When the dough is warm but not hot, stretch and knead it for about 3 minutes until glossy and elastic. Add the cooked sweetened red beans and knead again to distribute them evenly throughout the dough.

Dust your work surface with cooked glutinous rice flour. Place the mochi dough on top and dust the surface lightly. Roll into a log about 3 cm thick, then slice into small pieces (around 20 g each). Serve immediately or store according to preference.