Heat oil in heavy large saucepan over medium heat. Add leeks and carrot; sauté until vegetables are tender but not brown, about 8 minutes. Add broth and bring to boil. Add favas and green beans and simmer until almost tender, about 8 minutes. Add asparagus and 1/3 cup basil and simmer until all vegetables are very tender, about 7 minutes longer. Season soup with salt and pepper. Stir in 1/3 cup basil. Ladle soup into bowls. Serve, passing Parmesan separately, if desired.