In a high-speed blender, blend all ingredients till totally smooth.
Create a large, double layer of cheesecloth and hold it over a large mixing bowl, or hold a nut milk bag over a large mixing bowl. Pour the Brazil nut milk through the cheesecloth or bag and squeeze thoroughly. You can compost or discard the nut pulp.
Transfer the nut milk to an airtight container. It will keep in the fridge for about 3 days.