Preheat the oven to 350°F (175°C).
Cook the egg noodles according to package instructions until al dente. Drain and set aside.
Steam the broccoli florets until tender-crisp, about 4-5 minutes. Drain and set aside.
In a large saucepan, melt the butter over medium heat.
Whisk in the flour and cook for 1-2 minutes until lightly golden and smooth, stirring constantly.
Gradually whisk in the milk, continuing to whisk until the mixture thickens and is smooth, about 5-7 minutes.
Remove from heat and stir in garlic powder, onion powder, salt, and black pepper.
Add 1 cup of cheddar cheese and all of the mozzarella cheese to the sauce. Stir until the cheeses are melted and the sauce is smooth.
In a large mixing bowl, combine the cooked egg noodles, steamed broccoli, cooked chicken, and cheese sauce. Mix gently until evenly combined.
Transfer the mixture to a greased 9×13-inch baking dish.
Sprinkle the remaining 1/2 cup cheddar cheese evenly over the top.
In a small bowl, mix the grated Parmesan cheese with the breadcrumbs. Sprinkle this mixture evenly over the casserole.
Bake uncovered in the preheated oven for 25-30 minutes, or until the top is golden brown and the casserole is bubbly.
Remove from the oven and let it rest for 5 minutes before serving.