Preheat oven to 400℉ and grease a 9-by-13-inch baking dish with oil.
Add rice and broccoli to the bottom of the baking dish. If any of the broccoli florets are much larger than the other, you may want to cut them smaller.
Toss chicken pieces with 1/2 tsp salt, 1/2 tsp garlic powder, and a few grinds of black pepper. Distribute the seasoned chicken evenly over the rice and broccoli.
Heat olive oil in a sauce pan or small pot over medium-high heat, add chopped onion and a pinch of salt and cook until onion is golden brown, about 3 to 5 minutes.
Meanwhile whisk cornstarch/arrowroot into the chicken broth, making sure the cornstarch is dissolved.
Once onion is cooked stir in the Italian seasoning then add the broth. Whisk in the remaining salt, mustard, and lemon juice then bring up to a simmer to thicken a bit. Once sauce is bubbling, pour evenly over the ingredients in the baking dish. Use a spoon to even out the top of the dish.
Cover the baking dish with foil then bake for 30 minutes or until chicken is cooked. Remove foil then add cheese evenly over the top, if using. Return the dish to the oven for 5 minutes to melt the cheese or use the broiler to get a golden, crunchy top. Serve warm.