Cook quinoa according to package directions. When done cooking, transfer it to a large bowl and toss with a fork. Let cool for 30 minutes or so tossing every 5 minutes.
Add broccoli, chicken, mango, carrots, olives, roasted red bell peppers, parmesan and Feta cheese to quinoa, stirring to combine.
To make dressing, place oil, lemon, salt and pepper into a mason jar with a lid. Close lid and shake for 30 seconds or so until well combined. Pour over quinoa and stir to combine. Taste and add additional salt and pepper to taste. Serve room temperature or chilled.