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 2-3 minutes until fragrant and translucent.
Add the chicken pieces to the skillet. Season with salt, black pepper, dried thyme, and paprika. Cook for 6-8 minutes, stirring occasionally, until the chicken is cooked through and no longer pink inside.
While the chicken cooks, steam the broccoli florets until just tender, about 4-5 minutes. Drain and set aside.
In a large mixing bowl, combine the cooked brown rice, cooked chicken with onions and garlic, steamed broccoli, Greek yogurt, low-fat milk, and half of the shredded cheddar cheese. Mix well until all ingredients are evenly incorporated.
Transfer the mixture into a greased 9×13-inch baking dish. Sprinkle the remaining shredded cheddar cheese evenly on top.
Bake uncovered in the preheated oven for 20-25 minutes, or until the casserole is heated through and the cheese on top is melted and lightly golden.
Remove from the oven and let the casserole rest for 5 minutes before serving.