Heat oil in large pot or Dutch oven over medium; sauté onion, celery, and carrots 7-8 minutes until starting to soften.
Cook garlic 1 minute until fragrant, stirring constantly.
Add zucchini, tomatoes, broth, Italian seasoning, and bay; boil.
Reduce to medium-low; simmer 15 minutes, stirring occasionally.
Add cannellini, green beans, and pasta; simmer 10-12 minutes until pasta tender and green beans cooked through.
Cook spinach 2 minutes until wilted; remove bay and season with salt and pepper.
Serve hot with generous Parmesan and crusty bread. Leftovers keep up to 5 days.