Heat olive oil in a large soup pot or dutch oven over medium heat. Add diced onion, carrots and celery. Season with a pinch of salt and cook, stirring often, until veggies begin to soften; 3-4 minutes.
Add minced garlic, tomato paste, basil, oregano, thyme, bay leaves to the pot and cook for a couple of minutes, stirring often. Then add corn, green beans and zucchini. Continue to cook and stir for about 2 minutes. Season with a pinch of salt and pepper.
Pour in undrained tomatoes and chicken or vegetable broth. Turn heat to medium-high and bring soup to a boil. Cover and reduce heat to low. Simmer for 15-20 minutes or until vegetables are tender. Stir in fresh minced parsley.
Serve hot, with grated parmesan cheese and some crusty bread for dipping.