Preheat the oven to 375°F (190°C) and lightly grease a 9x13 inch baking dish.
In the prepared dish, combine 2 cups cooked chicken (shredded or diced), 1 cup diced cooked ham, and 1 cup shredded Swiss cheese; stir to distribute evenly.
In a medium bowl, whisk together 1 (10.5 ounce) can cream of chicken soup, 0.5 cup milk, 1 tablespoon Dijon mustard, and 0.25 teaspoon black pepper until smooth.
Pour the creamy sauce over the chicken and ham mixture in the baking dish.
Sprinkle 0.5 cup shredded Swiss cheese evenly over the sauce layer.
In a small bowl, toss 0.5 cup Panko breadcrumbs with 2 tablespoons melted unsalted butter until coated, then sprinkle over the cheese layer.
Bake for 25–30 minutes, until bubbly around the edges and the topping is golden brown and crispy.
Remove from the oven and let rest for 5 minutes before serving.