Layer half each of potatoes, onion, carrots, and ham in a greased 2-quart baking dish.
Combine soup, milk, and pepper.
Pour half of sauce over vegetable mixture in dish.
Layer remaining vegetables and ham over sauce; top with remaining sauce.
Cover and bake at 375°F for 1 hour.
Remove cover, and sprinkle with Parmesan cheese; bake an additional 10 minutes.