This recipe is adapted from "Mushroom Cookery" by Roseta Reitz. It's similar to Leek and Potato soup, with lots of mushrooms.
Trim and wash the leeks, be sure to get all the sand out.
Add olive oil to 4-quart pot and cook the leeks slowly, for 5 minutes, covered, stirring from time to time, until mushy.
Add 3 pounds of diced potatoes and 5 cups chicken broth. Cover and simmer the soup for 25 minutes. Add all spices. Add 1 pound of whole mushrooms and simmer, covered, for 10 more minutes.
Pour two cups of soup into a blender and blend for about a minute, using high speed. Add another cup and blend some more. Continue until half the soup is blended. Pour blended soup back into stock pot.
Thin the soup with the milk or cream, and slowly return to a boil. If a thinner soup is desired, add more milk.