Heat the oil in a large lidded pot over medium heat. Add the onion, carrot, and celery, cover the pot, and cook until the vegetables start to soften, about 6 to 8 minutes, stirring occasionally.
Stir in the garlic and cook 1 minute, stirring constantly.
Add the zucchini, yellow summer squash, diced tomatoes, vegetable stock, tomato paste, Worcestershire sauce, bay leaf, thyme, Italian herb seasoning, salt, and black pepper.
Bring the soup up to a boil, then turn heat down and simmer (covered) until the vegetables are tender, about 20 minutes, stirring occasionally.
Add the beans and cook until warm throughout, about 2 minutes.