In a large soup pot, combine the potatoes, onion, carrots, celery and broth over medium-high heat; bring to a boil. Reduce heat to low, cover and simmer until the potatoes are just tender- about 10 minutes.
Add the tomatoes, zucchini, green beans, peas, oregano, salt and pepper. Continue to simmer until the vegetables are tender- about 10 minutes longer. Remove the pot from heat. Top individual servings with 1 tablespoon fresh basil and 1 tablespoon cheese.
If you are preparing this recipe as GLUTEN-FREE, just be sure to use a brand of chicken broth that is known to be GF.