Preheat the oven to 375°F (190°C). Lightly grease a 9×13-inch baking dish.
Bring a large pot of salted water to a boil. Add the ziti pasta and cook according to package instructions until al dente, about 8-10 minutes. During the last 3 minutes of cooking, add the broccoli florets to the boiling pasta water. Drain pasta and broccoli and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat. Season the chicken pieces with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Add chicken to the skillet and cook until browned and cooked through, about 6-8 minutes. Remove from heat 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, stirring constantly.
Gradually whisk in the milk, ensuring no lumps form. Continue cooking and whisking until the sauce thickens and coats the back of a spoon, about 5-7 minutes.
Remove the sauce from heat and stir in the mozzarella cheese, cheddar cheese, Parmesan cheese, garlic powder, onion powder, Italian seasoning, remaining 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Stir until the cheeses melt and the sauce is smooth.
In a large mixing bowl, combine the cooked pasta, broccoli, cooked chicken, and cheese sauce. Mix gently until everything is evenly coated.
Transfer the mixture to the prepared baking dish and spread it out evenly.
Bake uncovered in the preheated oven for 20-25 minutes, or until the casserole is bubbly and the top is lightly golden.
Remove from the oven and let it rest for 5 minutes. Sprinkle with chopped fresh parsley before serving.