Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, diced ham, and 1 cup of Swiss cheese. Mix well and set aside.
In another bowl, mix the sour cream, cream of chicken soup, garlic powder, onion powder, black pepper, and salt until smooth.
Pour the creamy mixture over the chicken and ham. Stir until fully combined.
Transfer the mixture into a greased 9x13 inch casserole dish, spreading it evenly.
In a separate bowl, mix the breadcrumbs with the melted butter. Sprinkle the breadcrumb mixture evenly over the casserole.
Top with the remaining ½ cup Swiss cheese.
Bake in the preheated oven for 30-40 minutes, or until the casserole is bubbly and the breadcrumbs are golden brown.
Remove from the oven and let it cool for a few minutes before serving. Garnish with chopped parsley if desired.