Saute the leeks and onions in butter in a large pot over medium heat, stirring constantly, until tender; about 2-3 minutes.
Lower heat, add the mushrooms, and cook about 10 minutes longer, covered, stirring occasionally.
Raise heat to medium, stir in the flour, and cook for 2-3 minutes, then add the thyme, bay leaf, broth, salt, sugar, and pepper.
Simmer, partially covered, for about 10 minutes.
Cool the soup slightly; discard the bay leaf; then puree the soup in batches in a blender or food processor.
Return the pureed soup to the pan and add the cream.
Cook over low heat until just heated through, but do not boil.
Adjust seasonings if necessary, and serve garnished with parsley.
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