Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add diced onion and minced garlic, sauté for 3-4 minutes until softened.
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 cooked brown rice, cottage cheese, Greek yogurt, dried thyme, dried oregano, salt, and black pepper. Mix well.
Add the sautéed chicken, onions, garlic, chopped broccoli, and chopped carrots to the rice mixture. Stir to combine evenly.
Pour the chicken broth into the mixture and stir gently.
Transfer the entire mixture into a greased 9×13 inch casserole dish and spread evenly.
Sprinkle 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 15 minutes until the cheese is melted and bubbly and the chicken is cooked through.
Remove from oven and let the casserole rest for 5 minutes before serving.