Heat olive oil in a large pot over medium heat. Add onion, celery, and carrots, and sauté for 5-7 minutes until vegetables begin to soften.
Add minced garlic and cook for 1 minute until fragrant, stirring constantly to prevent burning.
Pour in vegetable broth and crushed tomatoes, then add kidney beans, white beans, basil, oregano, and Parmesan rind if using. Bring to a boil, then reduce heat and simmer for 20 minutes.
Add zucchini, green beans, and pasta to the pot. Simmer for 10-12 minutes until pasta is tender and vegetables are cooked through.
Stir in chopped spinach and cook for 2-3 minutes until wilted. Remove Parmesan rind if used.
Season with salt and black pepper to taste.
Serve hot with grated Parmesan cheese sprinkled on top and garlic breadsticks on the side.