Preheat the oven to 375°F (190°C).
Cook the orzo pasta according to package instructions until al dente. Drain and set aside.
Steam the broccoli florets until tender but still crisp, about 4-5 minutes. Drain and set aside.
Heat olive oil in a large skillet over medium heat. Add the chopped onion and cook until softened, about 3 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Add the chicken pieces to the skillet and cook until no longer pink in the center, about 6-8 minutes, stirring occasionally.
Sprinkle the flour over the chicken mixture and stir well to coat. Cook for 1-2 minutes to remove the raw flour taste.
Gradually whisk in the chicken broth and milk, stirring constantly until the sauce thickens, about 3-5 minutes.
Add salt, black pepper, and dried thyme to the sauce. Stir to combine.
Remove the skillet from heat and stir in the Greek yogurt, cooked orzo, and steamed broccoli until well combined.
Transfer the mixture to a greased 9×13-inch baking dish.
Sprinkle shredded cheddar, mozzarella, and Parmesan cheeses evenly over the top.
Bake uncovered in the preheated oven for 20-25 minutes, or until the casserole is bubbly and the cheese is melted and golden brown.
Remove from oven and let cool for 5 minutes before serving.