Heat 3 tablespoons olive oil in heavy large pot over medium heat. Add onions, carrot, and celery. saute until all vegetables are soft, about 12 minutes. Add 3 1/2 cups water, beans with cooking liquid, and tomato and bring to simmer. Reduce heat to mediumlow and simmer 25 minutes to blend flavors, stirring occasionally. Mix in pasta; bring to boil. Cook until pasta is just tender but still firm to bite, adding more water to soup by 1/2 cupfuls if very thick, about 10 minutes. Season soup with salt and pepper.

Ladle soup into bowls. Sprinkle with chopped green onions, drizzle with extra-virgin olive oil, and serve.