Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add chopped onion and sauté for 3-4 minutes until translucent.
Add minced garlic to the skillet and cook for 1 minute until fragrant.
Add the chicken pieces to the skillet and cook for 5-7 minutes until they are no longer pink on the outside.
Stir in chopped carrots, broccoli florets, frozen peas, dried thyme, dried oregano, salt, and black pepper. Cook for another 3-4 minutes to slightly soften the vegetables.
In a large mixing bowl, combine cooked brown rice, chicken broth, Greek yogurt, and half of the shredded cheddar cheese. Mix well.
Add the cooked chicken and vegetable mixture to the rice mixture and stir until evenly combined.
Transfer the mixture into a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the remaining shredded cheddar cheese evenly over the top of the casserole.
Cover the casserole dish with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake for an additional 10-15 minutes until the cheese is melted and bubbly.
Remove from the oven and let cool for 5 minutes before serving.