Preheat the oven to 375°F and lightly grease a medium baking dish.
Chop the cooked chicken and ham into bite-sized pieces.
Mix cream of chicken soup, milk, Dijon mustard, garlic powder, and black pepper until smooth.
Stir the chicken and ham into the creamy sauce, then mix in 1 cup of Swiss cheese.
Spread the mixture in the baking dish and top with remaining Swiss cheese.
Mix breadcrumbs with melted butter and Parmesan, then sprinkle over the casserole.
Bake for 25 to 30 minutes until hot, bubbling, and golden on top.
Broil for 1 to 2 minutes if a deeper golden topping is desired, watching closely.
Let the casserole rest for 5 to 10 minutes before serving warm.