Heat olive oil in a large pot over medium heat. Once hot, add onions, carrots, and celery and saute 5-6 minutes. Add garlic and saute 30-60 seconds, or until fragrant.
Pour in broth. Add the tomatoes, potatoes, parsley, bay leaves, thyme and pepper. Stir well and bring to a boil.
Cover and simmer until potatoes are tender, about 20-30 minutes. Add green beans, corn, and peas and simmer an additional 60-90 minutes, covered, stirring occasionally. Serve hot.