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.
Notes
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.