Preheat the oven to 375°F (190°C).
In a large mixing bowl, combine the shredded chicken, diced ham, Swiss cheese, garlic powder, Dijon mustard, and salt and pepper.
In a separate bowl, mix the heavy cream with half of the breadcrumbs.
Fold the cream and breadcrumb mixture into the chicken and ham mix until well combined.
Transfer the mixture into a greased 9x13 inch baking dish and spread evenly.
Sprinkle the remaining breadcrumbs over the top of the casserole.
Bake in the preheated oven for 25-30 minutes, or until bubbly and golden brown.
Let the casserole cool for 5-10 minutes before serving, then garnish with fresh parsley.