Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken and diced ham. Mix well.
In another bowl, whisk together the milk, sour cream, Dijon mustard, garlic powder, onion powder, black pepper, and salt until smooth.
Pour the milk mixture into the chicken and ham, and stir until everything is evenly coated.
In the prepared baking dish, layer half of the cooked chicken and ham mixture, followed by half of the Swiss cheese. Repeat the layers with the remaining mixture and cheese.
In a small bowl, combine the breadcrumbs with olive oil and mix until the breadcrumbs are coated. Sprinkle the breadcrumb mixture evenly over the top of the casserole.
Bake in the preheated oven for 30-40 minutes, or until the casserole is hot and bubbly, and the breadcrumbs are golden brown.
Allow to cool for a few minutes before serving. Garnish with fresh parsley if desired.
Optionally, you can add vegetables like spinach or broccoli for extra nutrition before layering the mixture.
If making ahead of time, store in the refrigerator before baking and add an additional 10 minutes to the cooking time if baking from cold.