Heat olive oil in a large pot over medium heat and sauté onion, carrots, and celery for 6-8 minutes until softened.
Add minced garlic and Italian seasoning, cooking for 1 minute until fragrant.
Pour in chicken broth and diced tomatoes, bring to a boil, then reduce heat and simmer for 10 minutes.
Add cannellini beans, zucchini, and shredded chicken, and simmer for another 5 minutes.
Stir in pasta and cook according to package directions until al dente, about 8-10 minutes.
Add fresh spinach and stir until wilted, season with salt and pepper to taste, and serve hot with grated Parmesan cheese.