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 for 3-4 minutes until bright green and slightly tender. Drain and set aside.
Heat olive oil in a large skillet over medium heat. Add the chopped onion and sauté for 3-4 minutes until translucent.
Add the minced garlic to the skillet and cook for 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.
Gradually whisk in the milk and chicken broth, stirring constantly until the mixture thickens, about 5-6 minutes.
Remove the sauce from heat and stir in the shredded cheddar cheese, mozzarella cheese, salt, black pepper, paprika, and dried thyme until smooth.
In a large mixing bowl, combine the cooked orzo, steamed broccoli, cooked chicken, sautéed onion and garlic, and cheese sauce. Mix well to evenly coat all ingredients.
Transfer the mixture to a greased 9×13 inch baking dish. Sprinkle the grated Parmesan cheese evenly over the top.
Bake in the preheated oven for 20-25 minutes until the casserole is bubbly and the top is golden brown.
Remove from the oven and let it rest for 5 minutes before serving.