In large bowl, combine potatoes, ham and 1½ cups cheese. Transfer to a greased 13x9-inch baking dish.
In same bowl, whisk eggs, milk, soup and mustard until well combined; salt and pepper to taste. Pour over potatoes. Top with remaining cheese.
Refrigerate, covered, several hours or overnight (no longer than 24 hours).
Bake, uncovered, in a preheated 350°F oven until knife inserted in center comes out clean (about 50-60 minutes). Let stand 10 minutes before cutting.