Heat the olive oil in a large cast iron skillet, or dutch oven, over medium heat. Stir in the onions, and let them cook 2-3 minutes, stirring occasionally, until tender. Stir in the garlic, and cook for about 30 seconds-- until fragrant.
Stir in the rice, soup, and 2 cups of broth. Bring to a boil, then reduce the heat down to medium low, and continue cooking until the rice is fully cooked, stirring occasionally, about 12-15 minutes. Add more broth, if needed, as the rice cooks. Taste and season the mixture with salt & pepper, to taste.
Return the heat to medium, and stir in the chicken, broccoli, and half of the cheese. Continue cooking until the broccoli softens a bit, stirring occasionally, about 3-4 minutes.
Sprinkle the remaining cheese evenly out over top of the skillet, and put it in the oven under the broiler- just until it's melted and begun to brown in spots.
Sprinkle the dish with parsley, if using, and serve.