Warm the olive oil in a large pot over medium-high heat. Stir in the onions, carrots, and celery, cooking for about 4 minutes. Add the minced garlic and sauté for an additional 30 seconds.
Pour in the chicken or vegetable broth, followed by the diced tomatoes, potatoes, parsley, bay leaves, and thyme. Season with salt and freshly ground black pepper to taste.
Bring the mixture to a boil and then incorporate the green beans. Reduce the heat to medium-low, cover the pot, and allow it to simmer for 20–30 minutes, or until the potatoes are almost tender.
Stir in the corn and peas, continuing to cook for another 5 minutes. Discard the bay leaves and serve the soup warm.