Spread all the bread slices, 1 side only, with the butter and mustard. Add the 2 slices of ham
and 2 slices of cheese to each of 4 bread slices. Cover with remaining bread to make a traditional sandwich.
In a large shallow bowl add the beaten eggs
and the whole milk
. Season with salt and pepper, to taste, and combine well. Dip each sandwich into the egg mixture making sure you cover the whole sandwich, including the sides. Place on a large platter until ready to cook. Heat the remainder of the softened butter in a large skillet. When the butter
has melted and the pan is very hot, add the sandwiches and cook turning once, until golden brown, about 4 to 6 minutes. Transfer to serving plates and serve immediately.