Bring salted water to a boil in a large Dutch oven. Add orecchiette and cook according to package directions until 3 minutes shy of al dente.
Add broccoli and carrots to the pot and continue cooking for 2 minutes. Stir in peas during the final minute of cooking. Reserve 1 cup of the pasta cooking water, then drain the pasta and vegetables together. Set aside.
Return Dutch oven to medium heat. Melt butter and sauté mushrooms until browned and most moisture has evaporated, 5 to 6 minutes. Add garlic and cook for 30 seconds, stirring constantly.
Pour in chicken bone broth and bring to a gentle simmer. Whisk in Alfredo sauce until smooth, then stir in Parmesan, Cantanzaro herbs, and black pepper.
Return pasta and vegetables to the pot; add cooked chicken. Toss gently until everything is evenly coated and heated through, 2 to 3 minutes. If the sauce is thicker than you’d like, stir in a splash of reserved pasta water until it reaches your desired consistency.
Taste and season with salt if needed. Garnish with parsley and additional Parmesan before serving, if desired.
