In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced white onion, celery, and carrots. Sauté for about 5 minutes, or until the vegetables are softened and the onion is translucent.
Stir in the diced zucchini and minced garlic. Cook for another 2-3 minutes, allowing the garlic to become fragrant.
Add the canned diced tomatoes, vegetable stock, and bay leaf to the pot. Bring the mixture to a gentle simmer.
Stir in the Italian seasoning and tomato paste. Mix well to combine all the flavors.
Once the soup is simmering, add the drained and rinsed small white beans, kidney beans, and frozen green beans. Bring the soup back to a simmer, then add the small shell-shaped pasta. Cook for about 10-12 minutes, or until the pasta is tender.
Remove the bay leaf and taste the soup for seasoning. Adjust with salt and pepper as needed. Garnish with freshly chopped parsley before serving.