Heat olive oil in a pot over medium heat. Cook and stir onion and carrots in hot oil until the onion is translucent, about 5 minutes. Add zucchini; continue cooking until the zucchini begins to soften, about 5 minutes more. Pour chicken broth over the zucchini mixture, place a cover on the pot, and bring to a boil and cook for 8 minutes. Stir spinach into the mixture; continue cooking until the zucchini is tender, about 2 minutes more.
Mash the zucchini mixture with a potato masher until a desired texture is achieved. Pour potato soup into the zucchini mixture; bring to a simmer and cook for 5 minutes. Stir half-and-half and Pecorino Romano cheese into the zucchini mixture; stir. Continue cooking until heated through completely, 2 to 3 minutes.
1/4 cup olive oil
1 1/2 onion, diced
2 carrots, diced
3 large zucchini, chopped small
1 (14.5 ounce) can fat-free chicken broth
1/2 (16 ounce) bag baby spinach leaves, chopped
1 (10.75 ounce) can cream of potato soup
1 quart fat free half-and-half
1/2 cup grated Pecor