Whisk together 1/4 cup soy milk and arrowroot until well incorporated. Then add the matcha until you have no clumps. Set aside.
Blend the rest of the ingredients (except the vanilla) in a blender until very smooth. Pour into a saucepan and bring to a boil. As soon as it boils, remove from heat immediately. Add in the matcha mixture and vanilla, let cool. Add mixture to a container with a lid and let chill in the refrigerator for at least 2 hours then move to freezer. As soon as ice crystals begin to form, remove and mix well to break up the crystals and return to the freezer. Repeat a few times to keep smooth, over 2-3 hours.