In a soup pot over medium heat, saute the leeks with a pinch of salt in olive oil until they are tender and translucent, about 5 minutes.
Add the garlic and potatoes and saute for 2-3 more minutes.
Add the broth or water to just cover the vegetables. Bring to a boil, cover, reduce heat, and simmer until the vegetables are soft, about 30-45 minutes.
Add the seasonings and wakame and simmer for 1 more minute. Puree the soup in a blender or directly in the pot with an immersion blender. Alternately, skip this step and serve the soup chunky.