Preheat your oven to 350°F (175°C).
Shred the cooked rotisserie chicken into bite-sized pieces and dice the cooked ham into small cubes.
In a large mixing bowl, combine the shredded chicken, diced ham, and shredded Swiss cheese. Mix well and transfer to a greased 9x13 inch baking dish.
In another bowl, whisk together the heavy cream, chicken broth, Dijon mustard, garlic powder, onion powder, black pepper, and salt until smooth. Pour this sauce over the chicken and ham mixture and stir gently.
Sprinkle the breadcrumbs evenly over the top and bake for 30-35 minutes until golden brown and bubbling. Let it cool for 5 minutes before serving.