Trim the fennel, reserving the feathery leaves. Cut across the heads, slicing the fennel into 1/4-inch rounds.Separate the rounds into strips . Pick out six attractive leaves and reserve for garnish. Tear remaining leaves into small pieces. Heat the oil in a large saucepan. Add the fennel, potato, and onion and toss to coat evenly. Cook and 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 boil. Reduce heat, cover and simmer 30 minutes, or until the potato is soft. Carefully transfer to a blender or food processor, cover the lid with a towel to prevent hot splatters, and puree. (Or use an immersion blender.) Stir in 1/2-cup of the yogurt and chill the soup thoroughly. When ready to serve, swirl 2 teaspoons yogurt on top of each bowl and trim with the reserved fennel leaves.