Preheat the oven to 350°F (175°C) and lightly grease a medium-sized baking dish.
In a large mixing bowl, combine the shredded chicken, softened cream cheese, shredded Swiss cheese, chopped ham, mayonnaise, sour cream, Dijon mustard, garlic powder, onion powder, and black pepper. Mix until all ingredients are evenly incorporated and the mixture is creamy.
Transfer the mixture to the prepared baking dish and spread it into an even layer using a rubber spatula.
In a small bowl, toss the panko breadcrumbs with the melted butter until evenly coated. Sprinkle the buttered breadcrumbs over the top of the dip.
Bake in the preheated oven for 20–25 minutes, or until the dip is hot and bubbly and the breadcrumbs are golden brown.
Remove from the oven and let it cool for 5 minutes before serving. The dip should be creamy with a crispy, golden topping.