In a large nonstick skillet, heat the oil. Add the zucchini, broccoli, and garlic; cook, stirring as needed, until tender-crisp, about 5 minutes.
Add tomatoes, basil, oregano, and rosemary; cook, stirring as needed, until the tomatoes are softened, about 5 minutes.
Meanwhile, cook the pasta according to the package directions. Drain, reserving 1/4 cup of the pasta water, and place pasta in a serving bowl. Add the vegetable mixture, cheese and the reserved pasta water; toss to combine.