Mix together the dressing ingredients and set aside.
Cook the pasta according to package instructions. Two minutes before the end of cooking, add the broccoli to the pot of boiling water to blanche it a little bit. Drain the pasta and broccoli together, then immediately run the pasta and broccoli under cold water to stop the cooking.
Fire up the grill on medium-high and cook the chicken until a thermometer registers an internal temperature of 165 °F . Alternatively, you can cook the chicken on the stovetop over medium-high heat, again until the thermometer registers an internal temperature of 165 °F . Let the chicken rest about 5 minutes before chopping it into bite-size pieces.
Add the chopped chicken, the bell pepper, grape tomatoes, red onion and Parmesan cheese to the pasta and broccoli. Stir in the dressing.