Using kitchen scissors, cut a 1/2-inch square from the center of each bread cube; don't cut through the bottom. Discard the squares. In a bowl, toss the hollowed-out bread cubes with the 2 tablespoons of melted butter. Arrange the cubes on a baking sheet and bake for about 8 minutes, until they are lightly toasted.
Increase the oven temperature to 425°. In a small saucepan, melt the remaining 2 tablespoons of butter. Add the flour and cook over moderate heat, whisking, until smooth, about 1 minute. Whisk in the milk until a thick paste forms. Remove from the heat and fold in the cheese and ham. Season with the nutmeg, salt and pepper. Spoon the cheese filling into the bread cubes. Bake for about 5 minutes, until the cheese is melted. Serve hot.