Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, diced ham, and half of the Swiss cheese. Mix well and set aside.
In a saucepan, combine the heavy cream, chicken broth, Dijon mustard, garlic powder, onion powder, salt, and pepper. Whisk together and heat over medium until just warmed, about 3-5 minutes.
Pour the cream mixture over the chicken and ham mixture, stirring to combine thoroughly.
Pour the entire mixture into a greased 9x13 inch casserole dish, spreading it out evenly.
In a separate bowl, combine the bread crumbs with olive oil, mixing until the crumbs are well-coated. Sprinkle the bread crumb mixture evenly over the casserole.
Top with the remaining Swiss cheese.
Bake in the preheated oven for 30-35 minutes, or until the casserole is bubbly and the top is golden brown.
Remove from the oven and let it cool for a few minutes before serving. Garnish with fresh parsley if desired.