Preheat the oven to 375°F (190°C).
In a large skillet, heat olive oil over medium heat. Add the chopped onion and minced garlic, sauté for 3-4 minutes until softened.
Add the chicken pieces to the skillet, season with salt, black pepper, paprika, and dried thyme. Cook for 5-7 minutes until the chicken is lightly browned but not fully cooked through. Remove from heat.
In a large mixing bowl, combine the uncooked rice, chicken broth, condensed cream of mushroom soup, milk, and shredded cheddar cheese. Stir until well combined.
Add the sautéed chicken, onions, and garlic mixture to the rice mixture. Stir to combine evenly.
Transfer the entire mixture into a greased 9×13 inch baking dish. Spread evenly.
Cover the baking dish tightly with aluminum foil and bake in the preheated oven for 40 minutes.
While the casserole is baking, bring a large pot of salted water to a boil. Add the trimmed green beans and cook for 4-5 minutes until tender-crisp.
Drain the green beans and toss them with butter, salt, and black pepper to taste.
After 40 minutes, remove the casserole from the oven and carefully remove the foil. Bake uncovered for an additional 5 minutes to allow the top to brown slightly.
Remove the casserole from the oven and let it rest for 5 minutes before serving.
Serve the chicken rice casserole hot with the buttered green beans on the side.