Place croutons in a greased 3-qt. baking dish. Sprinkle with cheese and ham. In a large bowl, whisk the eggs, 2 1/4 cups milk and mustard; pour over ham and cheese Cover and refrigerate over night.
Preheat oven to 350*.
Remove from the refrigerator 30 minutes before baking. Whisk soup, sour cream and remaining milk together until blended; spread over casserole. Top with hash browns; dot with butter and sprinkle with paprika and pepper.
Cover and bake for 30 minutes. Uncover and bake for 30 minutes more, until edges are browned. Let stand for 10 minutes before serving.