Heat the olive oil in a large pot over medium heat. Add the chopped carrots, celery, diced onion, salt, pepper, and cubed potato. Sauté for about 3 minutes.
Stir in the minced garlic and cook for an additional minute. Add the canned diced tomatoes, vegetable broth, and diced zucchinis.
Bring the mixture to a boil. Reduce the heat, cover the pot with a lid, and let it simmer for 45 minutes.
Add the rinsed and drained cannellini beans, fresh spinach, and elbow macaroni. Cover and simmer for another 10 minutes.