You can add extra salt if you prefer to omit the Parmesan cheese.
Bring large pot of lightly salted water to a boil. Add penne and stir occasionally to prevent sticking. Cook until just tender, about 10 minutes.
Meanwhile, in large deep skillet, heat oil over medium heat. Add garlic and shallots and cook, stirring, until lightly browned, 2 minutes. Add zucchini and squash and cook, stirring occasionally, until tender and golden at edges, about 6 minutes.
Drain penne, reserving 1 cup cooking water. Stir lemon peel, salt, pepper and reserved cooking water into squash mixture.
Transfer penne to large serving bowl. Add squash mixture, basil and chives and toss to combine. Sprinkle with Parmesan cheese if using and serve hot.