Cook pasta according to package instructions. Prepare zucchini sauce while pasta is cooks.
Peel and mince garlic.
Rinse and grate zucchini. Measure 2 cups grated zucchini.
In a large skillet over medium heat, heat oil. Add zucchini, shredded carrots , peas and minced garlic. Cook until mixture softens and zucchini yields some liquid, about 5 minutes.
Drain pasta, reserving ½ cup cooking liquid.
Add 1-2 teaspoons cooking liquid to zucchini mixture. Add drained pasta. Stir, coating pasta evenly with sauce. Add more pasta water as needed.
Transfer pasta to large bowl for serving. Sprinkle with grated Parmesan. Season with salt and pepper. Toss to combine.