Preheat oven to 350 degrees. Meanwhile, on the stovetop, heat the oil in a wide skillet and cook the onion until starting to brown, about 7 minutes. Add the cauliflower rice and continue cooking until cauliflower is also golden, about 7 more minutes. Add the broccoli and seasonings and cook until heated through.
Transfer to a bowl and stir in chicken, sour cream and 1 1/2 cups of the cheese. Transfer to a greased 8 by 8-inch baking dish, cover with foil and bake for 25 minutes. Remove foil, add remaining half cup of cheese and bake for another 10 minutes or until top is bubbling and golden.