A really simple soup to make, perhaps made complicated by using 3 separate types of potato. I simply use whatever variety I have grown in the garden. The previous comment suggests that the ppotatoes should be peeled and mashed. I will never peel a potato, so much goodness and flavour is lost if you do. Also my preference would be to leave the potato in chunks as it gives texture to the soup.
Some people suggest adding milk or cream, but that is not possible for a Vegan recipe, so have you tried "Oatly", this is a "milk" made from oats with no dairy content at all. Website http://www2.oatly.com