Preheat the oven to 350°F (175°C).
In a medium saucepan, bring the chicken broth to a boil. Add the uncooked rice, reduce heat to low, cover, and simmer for 15 minutes or until rice is tender and liquid is absorbed.
While the rice cooks, heat olive oil in a large skillet over medium heat.
Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic, diced green bell pepper, and sliced mushrooms to the skillet. Cook for 5 minutes, stirring occasionally, until vegetables are tender.
Stir in the frozen peas and carrots mix and cook for another 2 minutes. Remove from heat.
In a large mixing bowl, combine the cooked rice, sautéed vegetables, cooked shredded chicken, cream of mushroom soup, milk, salt, black pepper, dried thyme, and paprika. Mix well.
Stir in shredded cheddar cheese and half of the shredded mozzarella cheese.
Transfer the mixture to a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the remaining mozzarella cheese evenly over the top.
Cover the casserole dish with aluminum foil and bake for 30 minutes.
Remove the foil and bake for an additional 10-15 minutes until the cheese on top is melted and bubbly.
Let the casserole rest for 5 minutes before serving.