Preheat your oven to 375°F (190°C) and lightly grease a 9x13 inch baking dish with cooking spray.
Heat the olive oil in a skillet over medium heat. Add the diced onion and cook for 3-4 minutes until softened. Add the minced garlic and cook for another 30 seconds until fragrant. Remove from heat.
In a medium bowl, whisk together the chicken broth, Greek yogurt, dried thyme, salt, and pepper until smooth.
In a large mixing bowl, combine the cooked rice, cooked cubed chicken, broccoli florets, steamed carrots, sautéed onion mixture, and half of the shredded cheddar cheese.
Pour the sauce mixture over the ingredients and toss gently until everything is evenly coated.
Transfer the mixture to the prepared baking dish and spread it out into an even layer.
Top with the remaining shredded cheddar cheese.
Bake for 20-25 minutes, or until the cheese is melted and bubbly and the casserole is heated through.
Let the casserole rest for 5 minutes before serving to allow the sauce to thicken slightly.