Heat the olive oil in a large Dutch oven or heavy-bottomed soup pot over medium-high heat.
Add the chopped onion, carrots, and celery. Sauté for 5-7 minutes until the vegetables begin to soften.
Stir in the diced zucchini and minced garlic. Cook for an additional 2 minutes until the garlic is highly fragrant.
Pour in the diced tomatoes (with their juices), vegetable broth, rinsed beans, and Italian seasoning. Season with salt and black pepper. Bring the soup to a gentle boil.
Once boiling, stir in the dry pasta. Reduce the heat to a simmer, cover loosely, and cook for 10-12 minutes, or until the pasta is al dente (tender but firm to the bite).
Remove the pot from the heat. Immediately stir in the fresh spinach. The residual heat of the soup will wilt the spinach perfectly in just a minute.
Taste the broth and adjust the salt and pepper if necessary. Ladle into warm bowls and top with a generous sprinkle of grated Parmesan cheese before serving!