Evenly divide and spread the mustard on 4 slices of bread. Place a few slices of ham, followed by 2 slices of potatoes, 2 slices Cantal, and 1 tablespoon of Béchamel on the mustard-side of the bread. Cover the cheese with the remaining slices of bread and spread the butter on the outside surfaces of the sandwiches.
Place the sandwiches on an ungreased baking sheet and broil for about 5 minutes, turn them over, and continue cooking until they are crispy and golden brown, about 5 additional minutes. Spread the top of the sandwich with 1 tablespoon Béchamel and serve while hot.