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 and cook for 5-6 minutes until lightly browned but not fully cooked through.
Add the sliced mushrooms and chopped broccoli to the skillet and cook for an additional 3 minutes until vegetables begin to soften.
In a large mixing bowl, combine the cooked brown rice, low-fat cottage cheese, plain Greek yogurt, dried thyme, dried oregano, black pepper, and salt. Stir until well mixed.
Add the sautéed chicken and vegetable mixture to the rice mixture and stir to combine evenly.
Pour the chicken broth into the mixture and stir gently to incorporate.
Transfer the entire mixture into a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the shredded reduced-fat 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 and the casserole is heated through.
Remove from oven and let cool for 5 minutes before serving.