Heat a large soup pot or Dutch oven over medium heat and add 2 tablespoons of olive oil. Add the chopped onions and carrots, cooking for 6-8 minutes, stirring occasionally until they turn golden.

Stir in the celery, canned tomatoes with their juice, broth, potatoes, green beans, bay leaves, salt, and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for about 25 minutes.

Once the vegetables are tender, add the corn, peas, green onions, and parsley. Adjust the seasoning with salt, and let it simmer for another 5-8 minutes. Remove from heat and serve warm.