Reserve some of the fennel leaves to garnish the soup. Remove any tough or bruised outer leaves from the fennel bulb. Trim off the root end and the stems; discard. Thoroughly rinse the trimmed bulb and quarter the bulb lengthwise; remove and discard the core. Chop remaining fennel bulb.
In a 4-quart Dutch oven, heat olive oil and butter over medium-high heat. Add fennel, onion, and garlic. Reduce heat to medium-low and cook, covered, for 25 minutes, or until onions are tender, stirring occasionally. Uncover; cook and stir over medium-high heat for 3 to 5 minutes more or until unions are golden.
Add the undrained tomatoes, broth, tomato sauce, vegetable juice and dried basil. Bring to boiling; reduce heat. Simmer, covered, for 15 minutes more. Garnish each serving with the reserved fennel leaves. Makes 8 side-dish servings.