Preheat the oven to 375°F (190°C). Lightly grease a 9×13-inch casserole dish.
Bring a large pot of salted water to a boil. Add the orzo pasta and cook according to package instructions until al dente, about 7-8 minutes. During the last 3 minutes of cooking, add the broccoli florets to the pot with the orzo. Drain both orzo and broccoli and set aside.
In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1-2 minutes until lightly golden and bubbling, stirring constantly.
Gradually whisk in the milk, ensuring no lumps form. Continue to cook and whisk until the sauce thickens, about 5-7 minutes.
Remove the sauce from heat and stir in garlic powder, onion powder, salt, black pepper, dried thyme, and paprika.
In a large mixing bowl, combine the cooked orzo and broccoli, cooked chicken, and the sauce. Stir until everything is evenly coated.
Add half of the cheddar cheese, half of the mozzarella cheese, and half of the Parmesan cheese to the mixture. Stir to combine.
Transfer the mixture to the prepared casserole dish. Sprinkle the remaining cheddar, mozzarella, and Parmesan cheeses evenly over the top.
Bake in the preheated oven for 20-25 minutes, or until the casserole is bubbly and the cheese on top is melted and golden brown.
Remove from the oven and let it rest for 5 minutes before serving.