Preheat the oven to 375°F (190°C).
In a large skillet, heat olive oil over medium heat. Add the chopped onion and sliced mushrooms and sauté for 4-5 minutes until softened.
Add the minced garlic to the skillet and cook for 1 minute until fragrant.
Add the chicken pieces to the skillet and cook for 5-6 minutes until lightly browned but not fully cooked through.
In a large mixing bowl, combine the uncooked rice, chicken broth, sour cream, dried thyme, paprika, salt, and black pepper. Stir until well mixed.
Add the sautéed chicken, onions, mushrooms, and thawed peas to the rice mixture. Stir to combine evenly.
Transfer the entire mixture into a greased 9×13 inch baking dish and spread it out evenly.
Cover the baking dish tightly with aluminum foil and bake in the preheated oven for 35 minutes.
Remove the foil, sprinkle the shredded cheddar cheese evenly over the top, and bake uncovered for an additional 10 minutes until the cheese is melted and bubbly.
Remove from the oven and let the casserole rest for 5 minutes before serving.