Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, sliced ham, Swiss cheese, heavy cream, chicken broth, Dijon mustard, salt, and pepper.
Transfer the mixture to a greased 9x13 inch baking dish.
In a small bowl, mix the panko breadcrumbs with olive oil until the breadcrumbs are evenly coated.
Sprinkle the breadcrumb mixture over the casserole evenly.
Bake in the preheated oven for 35-40 minutes, or until the top is golden brown and the filling is bubbling.
Remove from the oven and let sit for 10 minutes before serving.