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 ½ 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.
