Warm the olive oil in a large Dutch oven over medium heat. Add the onion, carrots, and celery; cook for 6 to 8 minutes, stirring, until softened.
Stir in the garlic, zucchini, green beans, Italian seasoning, salt, and pepper; cook for 1 minute. Add the diced tomatoes and vegetable broth, scraping the bottom of the pot.
Bring to a gentle boil, then reduce to a steady simmer. Cook uncovered for 15 minutes, until the vegetables are nearly tender.
Stir in the cannellini beans and pasta. Simmer according to the pasta package time, usually 8 to 10 minutes, stirring occasionally so the pasta does not stick. Add a splash of broth if the soup gets too thick.
Turn off the heat and stir in the spinach or kale until wilted. Taste and adjust salt and pepper. Serve hot with Parmesan, if desired.