Preheat large deep skillet on medium-high heat. Add oil, onion and garlic; cook for 3 minutes, stirring frequently.
Add chicken, 1/4 teaspoon salt, 1/4 teaspoon black pepper and saute for 5 more minutes, stirring occasionally.
Add quinoa, chicken broth, remaining salt and pepper, then stir. Cover with a tight-fitting lid, bring to a boil, reduce heat to low and simmer for 12 minutes.
Now it's time to add vegetables. At this point quinoa should be cooked al dente. Add zucchini and broccoli. Stir, cover with a lid and cook on low-medium heat for 5 more minutes. Add grape tomatoes and parsley, stir and remove from heat. Serve hot.
Notes
Store: Refrigerate in an airtight container for up to 5 days. I don't recommend to freeze leftovers because this dish contains fragile vegetables that will be mushy upon thawing.