Pat the chicken breasts dry with paper towels. Cut them into cubes and sprinkle lightly with salt and pepper.
Heat the oven to 325 F. Heat the olive oil in a heavy skillet over medium heat. Add the chicken and stir.
Cook and stir the chicken until browned on all sides and just tender, or about 10 to 12 minutes total.
Add the heavy cream to the pan and stir to scrape up any browned bits.
Grease a 7-by-11-inch baking dish or 1 1/2-quart casserole with the vegetable oil. Add the grated cauliflower. Sprinkle the cauliflower lightly with salt and pepper, basil, thyme, and fresh parsley. If using, add the onion powder. Stir well to mix all the ingredients.
Top the riced cauliflower with the browned chicken, and drizzle all the cream and juices from the pan.
Top the casserole with the shredded cheddar cheese. Cover the casserole tightly with foil and bake for 15 to 20 minutes.