Here is a totally vegetarian version:
3 large russet potatoes, peeled and diced
6 cups water
1/2 tsp.kosher salt
1 large yellow onion, peeled and coarsely chopped
2 Tbs. unsalted butter or olive oil
2 cups vegetable stock
1 cup milk
1/2 tsp. crushed red pepper flakes
1/4 cup finely chopped Italian parsley
Put the diced potatoes and water in a 6 qt. pan; add salt and bring to a boil. Cover and cook potatoes until they are soft. Drain and save the water, straining out any potato chunks.
While the potatoes are cooking, cook the onion in butter or oil in a soup pot over low heat until onion is transparent and softened (about 5 minutes).
Put the potatoes, onions, stock and milk (in batches if necessary) into a blender (not a food processor) and puree. If you need more liquid, add some of the reserved potato cooking water.
When the potato is pureed, return it to the soup pot and cook over medium-low heat, stirring often. Add more reserved potato cooking water and/or more milk until the soup is the consistency that you like.
Add the pepper flakes and parsley, turn the heat down to simmer and cook 3 to 4 minutes to blend the flavors. Add more potato water and/or milk if soup is too thick. Taste and add more salt if necessary.