Butter the bread slices on one side. Assemble the sandwiches by placing two slices of breadbutter side down on the work surface. Divide the ham on the bread slices and cover with the remaining slices of bread, butter side up.
Preheat a broiler.
Grill the sandwiches in a nonstick frying pan over medium heat until golden.
Divide the white sauce over the tops of the sandwiches and sprinkle with the cheese. Place the sandwiches on a baking sheet and put under the broiler until the cheese melts and the top is golden.