In a large Dutch oven or pot, heat 2 tablespoons of the olive oil. Add the onion, garlic and rosemary and cook over moderate heat until the onion is softened. Add the carrots, parsnips, broccoli stems and squash and cook for 1 minute. Add the broth, season with salt and pepper and simmer until the vegetables are nearly tender, about 15 minutes.
Meanwhile, in a medium skillet, heat the remaining 2 tablespoons of olive oil. Add the pasta and cook over moderately high heat, stirring frequently, until it is deeply golden, about 4 minutes.
Add the toasted pasta and the lima beans to the soup; cook until the pasta and vegetables are tender, 5 to 6 minutes. Discard the rosemary. Stir the cheese into the soup and serve, passing extra cheese at the table.