Pre-heat the oven to 350°F.
In a large skillet, over medium heat, heat olive oil.
Season the chicken breasts with the salt and pepper.
Place in the prepared skillet and brown on both sides; about 4 to 5 minutes per side.
Once browned, remove from the heat and transfer to a large plate/platter; set aside.
In the same skillet, add chopped onion and minced garlic; sauté until they become translucent;about 3 minutes.
Add mushrooms and broccoli to the skillet; cook for another 5 minutes, stirring occasionally.
Stir in the long-grain rice; cook for 2 minutes, allowing the rice to absorb the flavors from the vegetables.
Pour in the chicken broth and heavy cream; stir well to combine all ingredients.
Place the browned chicken breasts back into the skillet, making sure they are well-covered with the rice mixture.
Transfer the skillet to the pre-heated oven and bake for 25 to 30 minutes, or until the chicken is cooked through and the rice is tender.
