Begin by cooking the pasta in a large pot according to package directions. Add the broccoli into the pasta pot 1 minute before turning off the heat. Drain, set aside.
While the pasta is cooking, Pour 1 tablespoon oil into a large pan. Add the onion and cook for 3-4 minute or until golden. Add the garlic and cook for just a few seconds then add the sliced chicken. Season with salt & pepper and cook the chicken for 5-7 minute or until browned.
Add the parmesan, cream, pesto, and salt & pepper. Simmer mixture for 2-3 minutes. Add the cooked pasta and broccoli. Stir until fully combined. Simmer for another 2-3 minutes. Remove from heat and garnish with more parmesan. Enjoy!