Trim outer stalks from fennel; cut bulb in half lengthwise, and remove cores. Cut each half vertically into thin slices.
Heat oil in a large saucepan over medium heat until hot. Add fennel, carrot, and garlic; cook 10 minutes or until tender, stirring often. Stir in broth and next 3 ingredients. Bring to a boil; cover, reduce heat, and simmer 15 minutes.
Stir in pasta and spinach. Bring to a boil; reduce heat, and simmer, uncovered, 5 minutes or until pasta is tender. Remove and discard bay leaf. Ladle soup into individual bowls; sprinkle each serving with 1 teaspoon cheese.