Because this soup contains no chicken or beef broth to offer competition, the pure flavors of fennel and tomato shine through.
1. Trim the fennel, reserving the feathery leaves. Cut across the heads, slicing the fennel into ¼-inch-thick rounds. Separate the rounds into strips. Pick out 6 attractive fennel leaves and set them aside for a garnish. Tear the rest into small pieces.
2. Heat the oil and butter in a large saucepan until the butter is melted. Add the fennel, potato, and onion and toss to coat evenly. Stir over medium heat until the onion is tender. Pour in the water. Add the fennel leaves tomatoes, thyme, salt, and cayenne. Bring to a gentle bubble. Cover and cook for 30 minutes or until the potato is soft.
3. Transfer to the container of a blender or processor and whirl until smooth. Return to the saucepan. Stir in the cream and heat until warmed through. Serve hot garnished with the 6 reserved sprigs of fennel leaves.