Heat the oil in a large Dutch oven over medium-high heat. Add the onion, carrot, celery, garlic, salt, rosemary, black pepper and crushed red pepper. Cook, stirring occasionally, until the vegetables are just tender, 8 to 10 minutes.
Stir in the broth, 2 cups water, the cannellini beans, tomatoes, zucchini and vinegar. Bring to a boil over medium-high heat; reduce the heat to medium low and simmer until the zucchini is just tender, about 10 minutes. Stir in the collard greens and simmer until the greens are tender, about 2 minutes. Stir in the orzo. Season with salt. Top with the shredded parmesan.
Photograph Courtesy of Time Inc. Books/Alison Miksch.