Toast bread. Mix ham, cheese, mayonnaise and ground mustard. Spread ham mixture over 6 slices of bread; top with remaining slices to make 6 sandwiches. Cut sandwiches into triangles.
In a greased 13x9-in. baking dish, arrange sandwich triangles cut side down, with points facing up, pressing together as needed to fit in 2 rows. Whisk eggs, milk, salt and pepper until well blended. Pour over sandwich triangles. Refrigerate, covered, overnight.
Remove casserole from refrigerator 30 minutes before baking. Preheat oven to 300°. Bake, uncovered, until a knife inserted in center comes out clean, 45-50 minutes.