Preheat your oven to 350°F (175°C).
In a large skillet, heat a tablespoon of olive oil over medium heat. Season the chicken breasts with salt and pepper and sear them on both sides until golden brown, about 4-5 minutes per side. Remove from skillet and set aside.
In the same skillet, add chopped onion and minced garlic. Sauté until translucent, about 3 minutes.
Add sliced mushrooms and broccoli florets to the skillet. Cook for another 5 minutes until they soften slightly.
Stir in the long-grain rice into the vegetable mixture and cook for about 2 minutes. Then pour in chicken broth and heavy cream, stirring until well combined.
Place the seared chicken breasts back into the skillet on top of the rice mixture. Transfer the skillet into the preheated oven and bake for 25-30 minutes until the chicken is fully cooked and rice is tender.
Garnish with fresh parsley before serving.