Melt butter in a large pot over medium heat. Add the onions and sweat, stirring occasionally, until translucent. Add the mushrooms and sauté for another 5 minutes, adding more butter as needed if the pan gets too dry. Add the chicken broth, parsley and thyme sprigs. Partially cover the pot with a lid, so some steam can still escape, and simmer for 30 minutes. After 30 minutes, remove from the heat and discard the parsley and thyme sprigs.
Using an immersion blender or working in batches in a standing blender, blend the soup until smooth. Return to the pot and season with salt and pepper to your taste. Depending on the stock you use, you may find that you do not need to add any salt. Rewarm over low heat if necessary.
To serve, ladle the soup into bowls and top each with a dollop of crème fraiche and a sprinkling of chopped parsley. You can also garnish with some quickly sautéed mushrooms if you prefer.