Preheat oven to 350ºF. Place chicken in a baking dish, and brush with olive oil. Season with salt and pepper.
Bake for 40 to 50 minutes or until a meat thermometer inserted into the center of the thickest breast registers 165ºF. Let cool. Chop chicken into bite-sized pieces.
Increase oven temperature to 400ºF. Cut cauliflower into florets. Pulse in a food processor until cauliflower resembles grains of rice or couscous.
Stir together cauliflower "rice," chicken, broccoli, sour cream, garlic powder, parsley, salt and pepper in a large bowl. Stir in mozzarella cheese and 1/2 cup Parmesan cheese.
Spread mixture in a 13x9-inch baking dish coated with cooking spray (or use two 8-inch square baking dishes).
Bake casserole for 45 minutes. Sprinkle remaining 1/2 cup Parmesan cheese over top, and bake 5 minutes longer or until browned.
Place casserole mixture in two 8-inch baking dishes, if desired. Bake one now, and freeze one for later or give the second casserole away.