Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with olive oil.
In a large mixing bowl, combine the shredded chicken, diced ham, and Swiss cheese. Mix well.
In a separate bowl, whisk together the milk, sour cream, Dijon mustard, garlic powder, black pepper, and salt until smooth.
Pour the milk mixture over the chicken and ham mixture. Stir until everything is well combined.
Transfer the mixture to the prepared baking dish, spreading it evenly.
Top the casserole with breadcrumbs, ensuring an even layer across the top.
Bake in the preheated oven for 30-35 minutes, or until the casserole is bubbly and the breadcrumbs are golden brown.
Remove from the oven and let it cool for 5 minutes before serving. Garnish with fresh parsley.