Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, diced ham, and shredded Swiss cheese.
In another bowl, whisk together the heavy cream, milk, Dijon mustard, garlic powder, and onion powder.
Pour the cream mixture over the chicken mixture and stir until well combined.
Transfer the mixture to a greased baking dish.
In a small bowl, mix the breadcrumbs with the melted butter. Sprinkle evenly over the casserole.
Bake for 40 minutes, or until the top is golden brown and the casserole is bubbly.
Let it cool for a few minutes before serving. Enjoy!