Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add chopped onion and minced garlic, sauté for 3-4 minutes until softened.
Add the chicken pieces to the skillet. Cook for 6-8 minutes until the chicken is no longer pink inside.
Add the sliced mushrooms and chopped broccoli to the skillet. Cook for an additional 4-5 minutes until vegetables are tender.
In a large mixing bowl, combine cooked brown rice, cooked chicken and vegetables from the skillet, low-fat cottage cheese, Greek yogurt, chicken broth, dried thyme, dried oregano, salt, and black pepper. Mix well to combine all ingredients evenly.
Transfer the mixture into a greased 9×13-inch baking dish. Spread evenly.
Sprinkle shredded reduced-fat cheddar cheese evenly over the top of the casserole.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake uncovered for an additional 10-15 minutes or until the cheese is melted and bubbly.
Remove from the oven and let the casserole rest for 5 minutes before serving.