Preheat oven to 350°F (175°C).
In a skillet over medium heat, melt butter and whisk in flour until a paste forms.
Gradually add milk, stirring continuously until the sauce thickens.
Stir in mustard powder, garlic powder, onion powder, salt, and pepper.
In a large bowl, combine shredded chicken, diced ham, Swiss cheese, and half of the Parmesan cheese.
Pour the sauce over the chicken and ham mixture and stir to combine.
Transfer the mixture to a greased baking dish.
Mix breadcrumbs with the remaining Parmesan cheese and sprinkle over the top of the casserole.
Bake for 25-30 minutes, or until the topping is golden brown and the casserole is bubbly.
Garnish with chopped parsley before serving.
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