Preheat the oven to 350°F (175°C). Grease the 9x13 inch baking dish with butter or cooking spray.
In a large mixing bowl, combine the sour cream, mayonnaise, milk, onion powder, garlic powder, salt, and black pepper. Whisk until smooth.
In the prepared baking dish, layer half of the uncooked egg noodles evenly across the bottom.
Spread half of the shredded chicken over the noodles, followed by half of the diced ham and half of the Swiss cheese.
Pour half of the creamy mixture over the layered ingredients in the baking dish.
Repeat the layers with the remaining noodles, chicken, ham, cheese, and pour the rest of the creamy mixture over the top.
In a separate bowl, mix the breadcrumbs with the melted butter until evenly coated. Sprinkle the breadcrumb mixture evenly over the casserole.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake for an additional 15 minutes, or until the top is golden and bubbly.
Allow the casserole to cool for a few minutes before serving.