Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the sour cream, cream of chicken soup, and onion soup mix. Whisk until well blended.
Add the uncooked rice into the mixture and stir until the rice is fully coated.
Pour the chicken broth into the bowl and mix well.
Lightly grease a 9x13 inch baking dish with olive oil.
Place the chicken breasts evenly in the baking dish. Season both sides with salt and pepper.
Pour the rice and soup mixture over the chicken breasts, spreading it evenly.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and sprinkle the shredded mozzarella cheese on top.
Bake uncovered for an additional 15 minutes, or until the chicken is cooked through and the cheese is bubbly and golden.
Remove from oven and let it sit for 5 minutes before serving. Garnish with fresh parsley if desired.