Heat olive oil in a large pot over medium heat. Add onions, carrots, and celery and saute 3 - 4 minutes then add garlic and saute 30 seconds longer. Pour in broth (if you want lesser ratio of broth use 3 cans then only 3/4 cup of the 4th can) and add tomatoes, potatoes, parsley, bay leaves, thyme and season with salt and pepper to taste (if you want a really flavorful soup you can add in more dried herbs, I prefer to let the flavors of the vegetables shine though and not overdue it). Bring to a boil, then add green beans, reduce heat to medium-low, cover and simmer until potatoes are tender, about 20 - 30 minutes, then add corn and peas and cook 5 minutes longer. Serve warm.