Preheat your oven to 350°F (175°C).
In a skillet over medium heat, add olive oil and sauté the diced onion for 3-4 minutes until soft. Add the minced garlic and continue to sauté for another minute.
Stir in the salt and black pepper, then add the shredded chicken to the skillet. Mix well to combine and remove from heat.
In a mixing bowl, combine the uncooked rice, chicken broth, peas, carrots, and heavy cream. Stir until well incorporated.
In the prepared baking dish, pour the rice mixture, then spread the sautéed chicken and onion mix evenly on top.
Cover the baking dish tightly with aluminum foil and place it in the preheated oven. Bake for 30 minutes.
Remove the foil from the baking dish, sprinkle the shredded cheddar cheese on top, and bake for an additional 10 minutes, or until the cheese is melted and bubbly.
Allow the casserole to cool for a few minutes before serving.