Heat a large pot over medium-high heat and add butter. Once melted, add in the onions, carrots and celery and sauté until onions are tender (about 4 minutes). Add in the garlic and sauté an additional 30 seconds, until fragrant.
Stir in the broth, tomatoes, potatoes, parsley, bay leaves, Italian seasoning, salt and pepper. Taste and adjust seasonings if desired. Bring mixture to a boil and then add in the green beans. Reduce heat to medium-low, cover and simmer until the potatoes and carrots are fork-tender (about 25 to 30 minutes).
Finally, stir in the frozen corn and peas and cook until heated through, about 5 more minutes. Remove the bay leaves and discard. Serve warm with crackers or toasted bread. Enjoy!
Feel free to swap in different veggies to your liking - broccoli, cauliflower, parsnips, peppers, etc.