While cutting chicken, boil a pot of salt water. When it is a rolling boil, add the pasta. At minute nine, add the chopped broccoli. When broccoli is cooked and pasta is al dente, drain the broccoli/pasta mixture.
Add the remaining tbs of butter to the drained pasta/broccoli mixture.
Turn on the pasta broccoli mixture to low on your stove and add the cup of cream, slowly, continuing to mix with a wood spoon.
Once the chicken strips and their "juice" are cooked through, add them to the pasta over low temperature. Add more grated parmesan to mixture and then add the previously prepared pesto to the pasta. Using a wood spoon mix everything together.
Add Salt and Pepper with a liberal hand, and ENJOY!