Heat the oil and water in a large soup pot over low heat. Add the leeks and carrots and cover to tenderize, but not brown, about 15 minutes.

When carrots are very tender, add in the chicken broth and bring to a boil. Add in the pasta and cook about 6 minutes. Put in the beans, broccoli, zucchini, yellow squash, green beans, peas, and asparagus. Reduce heat to medium and simmer uncovered until vegetables and pasta are tender, about 8 minutes. Season with the scallion, garlic, parsley, basil, lemon zest and pepper. Let simmer a couple more minutes until ready to serve. Add spinach and allow it to wilt. Ladle into bowls and top each bowl with 2 teaspoons of grated Reggiano Parmesan cheese. Additional broth may be needed when reheating this soup.