Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery. Sauté until vegetables begin to soften, about 7-8 minutes.
Add garlic and cook for 1 minute until fragrant, stirring constantly so it doesn't burn.
Stir in zucchini and green beans, cooking for another 3 minutes.
Add diced tomatoes with their juice, vegetable broth, Italian seasoning, and bay leaf. Bring to a boil.
Reduce heat to medium-low and add both types of beans. Simmer for 15 minutes.
Add the pasta and cook according to package directions (usually 8-10 minutes), stirring occasionally.
Stir in the fresh spinach during the last 2 minutes of cooking, allowing it to wilt. Remove bay leaf.
Season with salt and pepper to taste. Serve hot with a generous sprinkle of Parmesan cheese and fresh basil. Serve with crusty Italian bread for the full Maggiano's experience!