Cut off the feathery fennel tops; reserve some to garnish the soup. Remove any tough or bruised outer leaves from the fennel bulb. Trim off and discard the root end and stems. Quarter the bulb lengthwise; remove and discard core. Chop fennel.
In a 4-quart Dutch oven heat oil and butter over medium-high heat. Add chopped fennel, onion, and garlic. Reduce heat to medium-low. Cook, covered, about 25 minutes or until onion is tender, stirring occasionally. Cook, uncovered, over medium-high heat for 3 to 5 minutes or until onion is golden, stirring frequently.
Add tomatoes, broth, tomato sauce, vegetable juice, and basil. Bring to boiling; reduce heat. Simmer, covered, for 15 minutes.
Ladle soup into bowls. Garnish with the reserved fennel tops.