Pesto Penne with Roasted Chicken

This cooks up really fast and is yummy-freezes well

8 oz. Dried penne, mostaccioli or bow tie pasta (4 cups)
2 cups broccoli florets
1 7-oz. Container purchased basil pesto (about ¾ cup)
(I like to use even more of the pesto)
2 l/2 cups bite-size slices of purchased roasted chicken, refrigerated
cooked chicken breast strips or bite-size slices of leftover cooked
chicken (about 12 oz.)\
1 7-oz. Jar roasted red sweet peppers, drained and
cut into strips
¼ cup finely shredded Parmesan cheese
Finely shredded Parmesan cheese (optional)
½ tsp. Coarsely ground black pepper

Cook pasta according to package directions, adding broccoli the last 2 minutes of cooking. Drain, reserving ½ cup of the pasta water. Return drained pasta and broccoli to saucepan.
In a small bowl, combine pesto and the reserved pasta water. Add chicken, roasted red sweet peppers and pesto mixture to pasta in saucepan. Toss gently to coat. Heat through over medium heat. Add ¼ cup cheese to pasta mixture and toss to combine. Sprinkle with some additional Parmesan cheese and fresh pepper.