In a large heavy kettle, heat the olive oil over low heat for 1 minute; add the onions and cook, uncovered, for 5 minutes or until soft. Add the garlic and cook for 1 minute. Raise the heat to moderate and add the carrots, potato, squash, basil, oregano, and bay leaves. Cook, uncovered, 5 minutes longer, stirring occasionally.
Add the tomatoes and stock and bring to a boil; adjust the heat so that the mixture bubbles gently and cook, uncovered, 20 minutes longer. Add the green beans, cover, and cook until the beans are tender but still crisp--about 10 minutes. Remove the bay leaves.
Add the pasta and cook until tender. Add additional water, if necessary. Add the white beans. Cook 3 to 5 minutes longer, until heated through. Ladle into soup bowls and sprinkle with the cheese and parsley.
