Heat large pot of salted water to boiling over high heat. Add pasta and cook according to package directions for al dente. Add asparagus and broccoli to pot during last 1 minute of pasta cooking time (or last 2 minutes for softer cooked vegetables). Reserve 1 cup pasta cooking water, then drain everything and set aside.
Meanwhile, heat oil in large high-sided skillet over medium-high heat. Add chicken and cook 5 to 6 minutes or until golden brown and almost cooked through, stirring occasionally. Add garlic and peas; cook 1 minute.
Add pesto, grated Parmesan, lemon zest, salt, pepper, pasta, asparagus, broccoli and 1/2 cup reserved pasta cooking water to skillet; toss until well combined. Thin with additional pasta water if sauce is too thick.
Remove from heat; fold in mozzarella cheese. Serve immediately, garnished with pine nuts, basil leaves and shaved Parmesan.
The best prepared basil pesto from the grocery store is usually located near the refrigerated pasta like tortellini and ravioli (not the shelf stable jar of pesto in the boxed pasta aisle).
I most often buy the Buitoni brand, which is made with basil, Parmesan cheese and pine nuts. Rana brand is also good for pesto veggie pasta.
This website provides estimated nutrition information as a courtesy only. You should calculate the nutritional information with the actual ingredients used in your recipe using your preferred nutrition calculator.