Preheat oven to 400°F and grease a 9×13-inch baking dish with nonstick spray. Set aside.
Heat a large skillet over medium heat. Melt 1/4 cup of the butter, then add onions. Cook until translucent, about 5 minutes. Add garlic and cook one minute more.
Sprinkle flour over onions, cook one more minute, and then whisk in chicken broth and heavy cream. Bring to a slow boil, reduce heat, and continue cooking until mixture has thickened, about 5 minutes, stirring occasionally.
Season to taste with salt and pepper and stir in chicken, ham, cooked noodles, and Swiss cheese. Pour mixture into prepared baking pan.
Melt remaining butter in a microwave-safe bowl and then stir in breadcrumbs and Parmesan. Sprinkle breadcrumb mixture evenly over casserole.
Bake until hot and bubbling and breadcrumbs have browned, 30 minutes. Let cool 5 minutes before serving. Enjoy!
