In a large pot or Dutch oven, melt 2 tablespoons of butter over medium heat. Once melted, add the chopped onion and sauté for about 5 minutes until it becomes translucent. Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
Next, add the sliced carrots, chopped celery, and diced potatoes to the pot. Stir well to combine, allowing the vegetables to soften slightly for about 5 minutes.
Pour in 8 cups of low-sodium chicken stock or veggie stock, and add the canned diced tomatoes (with their juices). Stir everything together, ensuring the ingredients are well mixed.
Add the bay leaves, Italian seasoning, salt, and black pepper to the pot. Bring the soup to a gentle boil.
Once boiling, reduce the heat to low and let the soup simmer for about 20 minutes. This allows the flavors to meld beautifully.
After 20 minutes, add the green beans, frozen corn, and frozen peas. Stir gently and continue to simmer for an additional 10-15 minutes, or until all the vegetables are tender.
Before serving, remove the bay leaves and stir in the chopped parsley for a fresh touch. Taste the soup and adjust seasoning if needed.