Prepare spaghetti according to package directions.
Meanwhile, prepare chicken in the microwave according to package directions; set aside.
Place frozen broccoli in microwave and cook according to package directions.
When pasta is almost done, add pesto and chicken broth, stirring well. Add in chicken, cooked broccoli, and 1/2 cup Parmesan cheese. Serve hot with additional Parmesan cheese on top.