Measure the dry ingredients into a large bowl.
Add the milk.
Whisk until you have a smooth batter.
Steam the batter for 20 minutes on high heat. If you have a steam oven, you can place the whole bowl into the oven. Otherwise, transfer the batter to a bowl which will fit into a stove-top steamer.
Alternatively, cover the bowl with plastic wrap, poke a few holes in the plastic, and microwave the batter on high power for 3 minutes. Stir with a wooden spoon, and microwave for another 3 minutes until the dough is cooked through.
Once the mochi dough is cooked, it should have set completely and be firm and bouncy to the touch. Use a wooden spoon to mix the dough to check that it is cooked through. If you see any liquid, cook the dough for a bit longer.
While the mochi dough is still hot, beat in the butter with a wooden spoon. Keep beating until all of the butter is incorporated.
When the mochi dough is cool enough to handle (but not cold), use your hands to knead the dough into a soft ball. I recommend wearing food-safe disposable gloves for this task because the dough is very sticky.