Add milk, sugar, cornstarch, glutinous rice flour, and cocoa powder to a heatproof bowl. Whisk until the mixture is smooth and well combined.
Cover the bowl with a heatproof plastic food wrap. Use a toothpick to poke about 16 holes on the wrap.
Steam the mixture over high heat for 30 minutes. (Or you can microwave it for 3 minutes. Take out to check the texture. Poke a toothpick into the mochi, if the toothpick tip is dry, the mochi is fully cooked. If the toothpick tip is wet, cover the food wrap back, and microwave for 30 more seconds. )
Take the bowl out from the steamer/microwave, put 30g butter on the top of the steamed mochi dough. The mochi dough is very hot now, the butter will be melted quickly.
Mix the butter and the mochi dough with a spoon. Once the mochi dough is not too hot to be touched, use your hands to knead the dough until all the butter has been absorbed. You can put non-stick food handling gloves to avoid from getting sticky. If the dough is still to sticky to be kneaded, wrap up the dough with plastic food wrap, keep the dough in the fridge for 2 hours until it completely cools down. It will be much less sticky after it's cooled.
Knead the mochi dough by pulling and folding it for about 5 minutes, until you can pull it as long as your forearm (about 10 inches).
Transfer the mochi dough on a nonstick silicone mat, or a working surface covered with plastic food wrap. Apply some cooked glutinous rice flour on the surface of the mochi dough to prevent from getting sticky.
Cut the mochi dough into 6 equal portions. Flatten each small dough into 5-inch diameter circles. Cover with plastic food wrap and set aside.