Cook the chicken and onion: In a large, oven-proof skillet, heat olive oil over medium heat. Add chopped onion and cubed chicken, cooking for about 5 minutes until the chicken is no longer pink and begins to brown. Season with salt and pepper to taste. Stir in the minced garlic, cooking for an additional 30 seconds until fragrant.
Incorporate the rice and liquids: Stir in the uncooked rice, cream of chicken soup, and 2 cups of chicken broth. Bring this mixture to a boil, then lower the heat. Cover the skillet and let it simmer on medium heat for around 15 minutes, stirring occasionally until the rice is tender. Add more broth if necessary to ensure the rice cooks through.
Add broccoli and cheese: Once the rice is cooked, mix in the broccoli florets and half of the shredded cheddar cheese. Cook for an additional 2 minutes, allowing the broccoli to soften slightly.
Broil to finish: Sprinkle the remaining cheddar cheese over the top and place the skillet under the broiler for a few minutes, just until the cheese melts and turns golden brown.
Garnish and serve: Finish by garnishing with fresh chopped parsley. Serve immediately and enjoy.