Grease a large (enough to hold 6 slices of bread in one layer without over lapping) shallow pan with butter.
Cut crust off bread and place 6 slices in bottom pan. Cover with cheese slices and spread with mustard. Place ham evenly over top. Butter remaining bread slices and place buttered side up on top of ham.
Beat eggs slightly. Add milk and salt. Pour mixture over sandwiches. Let stand several hours so mixture is absorbed into bread.
Bake at 300° for 1 hour.
Cut into 6 squares and dish out with an egg turner or spatula.