Carefully peel the stems of the broccoli, then cut the whole bunches into small chunks. Bring the broth to a boil, add the broccoli, and cook it until it falls apart. Puree the soup in a blender or put it through a food mill, and let cool. Add the heavy cream.
Set the soup aside if it is not to be served immediately, and refrigerate when cool. When ready to serve, reheat, being careful