Heat oil in a medium saucepan and add sliced leek and salt. Cook for 2-3 minutes until soft. Slice wakame into thin strips. When leeks are soft, add water or stock, carrots and wakame. Bring soup to a boil and then reduce heat and simmer for 25 minutes, with the lid on.
Wash and chop greens and add to broth 5 minutes before the end of cooking. Place miso into a bowl and add a few tablespoons of the broth. Mix into a paste and add back to the soup.
Allow soup to stand for a few minutes and serve garnished with parsley.