Preheat oven to 180°C (350°F).
Grease a baking dish lightly with butter or oil.
In a large bowl, combine cooked chicken, ham, and pasta or rice.
Add Swiss cheese and mozzarella cheese and mix well.
In another bowl, whisk together cream of chicken soup, milk, garlic powder, and black pepper.
Pour the sauce over the chicken mixture and stir until evenly coated.
Transfer the mixture into the prepared baking dish.
Mix breadcrumbs with melted butter and sprinkle over the top.
Bake for 30–35 minutes until bubbly and golden brown.
Remove from oven, let rest for a few minutes, then serve warm.