Preheat the oven to 350°F (175°C).
Steam the broccoli florets until tender but still crisp, about 4-5 minutes. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add the chopped onion and cook until translucent, about 3-4 minutes.
Add the minced garlic to the skillet and cook for an additional 1 minute until fragrant. Remove from heat.
In a large mixing bowl, combine the cooked chicken, steamed broccoli, cooked onions and garlic, cream of mushroom soup, sour cream, milk, shredded cheddar cheese, shredded mozzarella cheese, salt, black pepper, and paprika. Mix well until all ingredients are evenly incorporated.
Transfer the mixture to a greased 9×13-inch baking dish and spread evenly.
In a small bowl, mix the panko breadcrumbs with melted butter until the crumbs are evenly coated.
Sprinkle the buttered panko breadcrumbs evenly over the top of the casserole.
Bake in the preheated oven for 35-40 minutes, or until the casserole is bubbly and the panko topping is golden brown.
Remove from the oven and let cool for 5 minutes before serving.