Set aside 2 of the mushrooms for garnish.
In a blender or food processor, whirl half the remaining mushrooms, 2 cups of the broth, and 2 tablespoons of the tarragon until mushrooms are finely chopped.
Pour into a 3- to 4-quart pan.
Repeat to puree remaining mushrooms with remaining 2 cups broth; pour into pan.
Bring broth mixture to a boil over high heat.
Reduce heat, cover, and simmer until mushrooms are soft about 10 minutes.
Add cream and stir just until hot.
Ladle soup into bowls.
Slice reserved mushrooms; sprinkle mushroom slices and remaining 2 tablespoons tarragon over soup.
Makes 4 servings.