Heat your oven to 350°F (175°C) and prepare a 9x13 inch baking dish by greasing it.
In a large bowl, toss together the shredded chicken, diced ham, and 1 ½ cups of the Swiss cheese.
In a smaller bowl, blend sour cream, milk, Dijon mustard, garlic powder, onion powder, salt, and pepper until smoothly combined.
Pour this creamy mixture over the chicken and ham, stirring carefully until all ingredients are evenly coated.
Transfer everything into the baking dish and spread it out evenly.
Scatter the remaining ½ cup of Swiss cheese on top.
If using, combine bread crumbs with melted butter and sprinkle this over the cheese layer.
Bake in the oven for about 25 to 30 minutes, or until the casserole is hot throughout and the cheese has melted and is bubbly.
Allow the casserole to rest for a few minutes before slicing and serving.