Place ice water in a large bowl that can hold a pot. Set aside.

In a small bowl, add 1/4 cup of milk and green tea powder, and whisk well (the powder may not dissolve completely). Then add back to the rest of milk (1 3/4 cups) and mix.

Heat the milk mixture and 1/2 cup of heavy cream at medium heat, and cook until just before boiling.

In a medium bowl, whisk the rest of the heavy cream (1/2 cup), yolks, and sugar. Add hot milk very slowly to the egg mixture.

Put egg/milk mixture back to the pot and cook at medium heat stirring constantly until thick (to check the thickness, dip a wood spoon in the egg/milk mixture, and check and see if you can scrape a clear line on the back of the spoon with a finger).

Place the pot in the ice water and cool. Transfer to a container and chill at least 3 hours in the refrigerator.

Follow the direction of your ice cream machine and mix. Very soft ice cream is done after about 15-20 minutes. Freeze 3 hours before serving.