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 for 4-5 minutes until tender-crisp. Drain and set aside.
In a large skillet, melt the butter over medium heat. Add the chopped onion and minced garlic and sauté for 3-4 minutes until softened.
In a large mixing bowl, combine the cooked chicken, steamed broccoli, cooked egg noodles, sautéed onion and garlic, cream of mushroom soup, sour cream, mayonnaise, shredded cheddar cheese, shredded mozzarella cheese, salt, black pepper, and paprika. Mix well until all ingredients are evenly incorporated.
Transfer the mixture into a greased 9×13-inch baking dish and spread it evenly.
Sprinkle the grated Parmesan cheese evenly over the top of the casserole.
Bake uncovered in the preheated oven for 30 minutes or until the casserole is bubbly and the top is golden brown.
Remove from the oven and let it rest for 5 minutes before serving.