Line a 5-inch square pan with parchment paper. Use any small pan, 4x6 (lol, does anyone have a pan this size?)
Add the mochiko and sugar to a large microwave-safe bowl, and then add about 1/3 of the milk. Stir the mixture together until there are no lumps. Add the remaining milk and continue stirring until it is smooth.
Put the bowl, uncovered, in the microwave and set it to cook for 2:30. If you have a 600 watt microwave, use full power. Adjust accordingly.
Remove the bowl from the microwave and stir the mixture until it's mostly smooth.
Add the butter and stir until fully melted and incorporated.
Microwave uncovered for another 3:00-3:30. Get to know your microwave!
Carefully remove the bowl from the microwave. Use a silicone spatula to knead the mochi together. The mochi is very hot, do not get it on your hands as you stir. The mixture will get very sticky and turn a translucent yellowish-white color as you knead it. If this doesn't happen, microwave it for another minute or two.
Transfer it to the prepared parchment-lined pan and press the butter mochi into the corners and flatten off the top.
Chill the mochi in the refrigerator for a few hours to firm it up. Unmold the butter mochi and peel off the parchment paper. Use a sharp knife to cut it into approximately 1" squares and then dust each piece liberally with potato starch. Brush the excess starch off and serve.