01 - Preheat the oven to 375°F and grease a 9x13-inch baking dish.
02 - Melt butter in a medium saucepan over medium heat. Whisk in flour and cook for 1 to 2 minutes until lightly golden. Gradually whisk in milk and cream until smooth.
03 - Stir in Dijon mustard, garlic powder, onion powder, white pepper, and salt. Cook, whisking constantly, until thickened, about 3 to 4 minutes. Remove from heat.
04 - Layer diced chicken evenly in the prepared dish, then top with diced ham. Sprinkle shredded Swiss and Gruyère cheeses over the top.
05 - Pour the warm cream sauce evenly over the layered ingredients.
06 - Combine breadcrumbs, melted butter, Parmesan cheese, and parsley in a bowl. Stir to moisten evenly.
07 - Sprinkle the breadcrumb mixture evenly over the casserole surface.
08 - Bake uncovered for 30 to 35 minutes until the topping is golden and bubbling.
09 - Allow to cool for 10 minutes before serving.