Preheat the oven to 350°F.
Lightly grease a baking dish with nonstick cooking spray or butter.
In a large mixing bowl, combine the dry stuffing mix, shredded Swiss cheese, fresh cut asparagus, and cubed cooked ham.
Stir until the ingredients are evenly distributed.
In a separate large bowl, whisk together the cream of mushroom soup, milk, eggs, and Dijon mustard.
Whisk until the mixture is smooth and fully combined.
Pour the soup and egg mixture over the stuffing, cheese, asparagus, and ham mixture.
Stir well until all ingredients are evenly coated and the stuffing mixture is fully moistened.
Transfer the mixture to the prepared baking dish.
Press the mixture firmly and evenly into the dish.
Bake for 45 minutes, or until the casserole is hot, set in the center, and lightly golden on top.
Remove the casserole from the oven.
Allow it to rest for a few minutes before serving.
Serve hot.