Cook the pasta according to package directions. Rinse with cold water until cool. (I usually add a few ice cubes to the strainer as well, to speed up the cooling process.)
While the pasta is cooking, wash the broccoli and chop into small florets. Dice the onion, using a handheld chopper if you have one, into very fine pieces.
In a medium bowl, whisk the mayo, sugar, and apple cider vinegar until well combined.
Place the cooled pasta and shredded chicken into a large bowl and mix until combined. Add the cheddar cheese, broccoli, and onion to the same bowl, mixing well.
Pour the mayo dressing over the salad mixture and stir until everything is well coated.
Refrigerate until ready to serve.