Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch casserole dish.
Cook the orzo pasta according to package instructions until al dente. Drain and set aside.
Steam the broccoli florets until just tender, about 4-5 minutes. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes.
Add the minced garlic to the skillet and cook for an additional 1 minute until fragrant. Remove from heat.
In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1-2 minutes to form a roux, stirring constantly.
Gradually whisk in the whole milk, continuing to whisk until the sauce thickens and is smooth, about 5-7 minutes.
Stir in garlic powder, onion powder, salt, black pepper, and dried thyme into the sauce.
Remove the sauce from heat and stir in 3/4 cup of shredded cheddar cheese and 1/4 cup of Parmesan cheese until melted and smooth.
In a large mixing bowl, combine the cooked orzo, steamed broccoli, cooked chicken, sautéed onion and garlic, and cheese sauce. Mix gently until evenly combined.
Transfer the mixture into the prepared casserole dish. Sprinkle the remaining cheddar cheese, mozzarella cheese, and Parmesan cheese evenly over the top.
Bake in the preheated oven for 25-30 minutes, or until the casserole is bubbly and the cheese topping is golden brown.
Remove from the oven and let the casserole rest for 5 minutes before serving.