Cut them lengthwise in half or quarters (depending on size) and then rinse well to get rid of any sand or soil still clinging to them.
Using only the white and light green portions, thinly chop the leeks.
Melt butter over low heat in a heavy soup pot; add the chopped leeks, cover the pot, and cook on low for about 10 minutes or until the leeks are softened but not browned.
Occasionally remove the lid and stir the leeks gently to check for browning.
Add broth, potatoes, salt, pepper, marjoram, thyme, and the bay leaf.
Simmer the soup for 20 minutes, stirring occasionally, until the potatoes are soft.
Using a potato masher or ricer, mash the soup to break up some of the potatoes and make a creamier soup.
You can mash more or less depending on how chunky you like your soup.
Add the cream and heat but don’t boil.
Taste and add more salt and pepper if desired.
Ladle soup into individual bowls and eat plain or garnish with croutons, a dollop of sour cream, or shredded Parmesan or Cheddar cheese.