1In ungreased 13x9-inch (3-quart) glass baking dish, arrange half of the bread slices, overlapping as needed. Brush bread in dish with mustard. Top evenly with ham and Swiss cheese, overlapping as needed. Top with remaining bread slices, arranging them over first layer of bread slices to make sandwiches.
2In medium bowl, beat eggs and milk with wire whisk until well blended. Carefully pour over sandwiches. Cover; refrigerate at least 1 hour but no longer than 12 hours.
3Meanwhile, in small bowl, mix Parmesan cheese, bread crumbs, parsley and butter. Set aside.
4Heat oven to 375°F. Sprinkle crumb topping over casserole. Bake uncovered 30 to 35 minutes or until sandwiches are puffed and golden brown.