Heat olive oil in a large deep skillet or sauté pan over medium heat.
Add the chicken pieces and cook for 5-7 minutes, stirring occasionally, until lightly browned and cooked through. Remove chicken from the pan and set aside.
In the same pan, add diced onion and cook for 3 minutes until softened.
Add minced garlic, sliced mushrooms, and chopped carrots to the pan. Cook for 5 minutes, stirring occasionally, until vegetables begin to soften.
Stir in the rinsed rice, coating it with the vegetables and oil for 1 minute.
Pour in the chicken broth and add dried thyme, dried parsley, salt, and black pepper. Stir to combine.
Bring the mixture to a boil, then reduce heat to low and cover the pan with a tight-fitting lid.
Simmer for 18-20 minutes, or until the rice is tender and most of the liquid is absorbed.
Stir in the cooked chicken, frozen peas, and heavy cream. Cook uncovered for 3-5 minutes until peas are heated through and the casserole is creamy.
Sprinkle shredded cheddar cheese evenly over the top. Cover the pan and let it sit off the heat for 2 minutes until the cheese melts.
Serve hot.