Cook the noodles according to the package directions. Drain, but do not rinse.
Meanwhile, prepare the pesto sauce, zucchini, and chick’n. For the pesto sauce, combine the basil, pine nuts, garlic, olive oil, nutritional yeast, 1 teaspoon salt and red pepper flakes, and pulse until smooth. Transfer the pesto to a large bowl, along with the vegan mayo, lemon juice and lemon zest, and whisk to combine. Add the cooked noodles to the bowl, tossing to combine. Set aside.
Melt 2 teaspoons of vegan butter in a nonstick skillet over medium-high heat. Add the zucchini in a single layer, and cook, not touching them, until the bottom sides brown and start to crisp on the outer edges, about 3 to 5 minutes. Season with a teaspoon of salt and fresh ground black pepper, give it a good mix and continue to cook another 2 to 3 minutes. Add the zucchini to the large bowl with the pasta.
In the same skillet you cooked the zucchini in, melt the remaining teaspoon of butter over medium heat. Once it’s melted add the chick’n strips and sauté, stirring often, until heated through, about 4 to 5 minutes. Add the chick’ strips to the large bowl, along with the peas and parmesan shreds. Toss gently to combine, ensuring all the ingredients are lightly coated in sauce.