Preheat oven to 375F.
Grease a casserole dish with cooking spray.
Layer quinoa on the bottom of the casserole dish.
Top with frozen broccoli and set aside.
Heat olive oil in a frying pan.
Add chicken cubes and cook for 1 to 2 minutes, or until browned on all sides.
Transfer chicken to the casserole dish. Set aside.
Place a saucepan over high heat; add chicken broth and flour and whisk and cook until smooth, about 1 minute.
Whisk in milk, garlic powder, cayenne pepper, chili powder, salt and pepper; continue to cook for 3 to 4 minutes, or until thickened.
Pour sauce over the chicken-mixture in the casserole dish; mix to combine.
Sprinkle cheeses on top and cover with foil.
Bake for 35 to 40 minutes, or until the quinoa is thoroughly cooked.
Remove from oven and let stand few minutes.