Melt the butter in a large stock pot or Dutch oven over medium heat. Add the chopped leeks, potatoes onion, bay leaf and garlic and cook, stirring often, until the leeks are tender, about 10 minutes.
Next add thyme, chicken stock, water, turn up the heat to high and bring it to a boil, drop the heat to a simmer and cook for 15 minutes, or until the potatoes are very soft.
Remove and discard the bay leaf. Using an immersion blender, blend the soup directly in the pot until smooth. (Alternatively, carefully transfer the soup content to the base of a blender( blend in batches if needed) cool the soup briefly, and blend until smooth. Then return it to the pot.)
Stir in the parmesan and cream, until the cream is warmed through. taste and season if needed.
Ladle the soup into bowls and garnish with parmesan and chives or parsley, if using.