Step 1Bring 1 quart of water to boil. Place the cannellini beans in a medium bowl, and pour the boiling water over them to cover. Allow the beans to stand one hour, then drain. Set aside.
Step 2In a large saucepot, heat 1 tablespoon olive oil over medium-low heat. Stir in the onions, carrots and celery and saut? until tender, about 8 to 10 minutes. Stir in the garlic, and saut? just until fragrant but not browned, about 30 seconds.
Step 3Stir in the chicken broth along with the drained beans and the sprig of rosemary. Bring the soup to a boil over high heat, then reduce the heat to a simmer. Partially cover the pot and simmer for 45 minutes.
Step 4Stir in the potatoes, then cover and simmer for 15 minutes. Stir in the zucchini and tomato, cover and continue to simmer 10 more minutes.
Step 5Season the soup to taste with salt and pepper. Ladle the soup into bowls and sprinkle each serving with fresh basil and a light drizzle of olive oil. Serve immediately.