Heat butter in a pot and sauté flour in it. Add milk bit by bit while stirring. Season with salt and pepper. Put the mixture in a cool place for 3-4 hours. Dice ham very finely and stir into the flour mixture.
Form 16 small croquettes with your hands. Beat the egg. Turn the croquettes first in the egg, then in breadcrumbs. Heat oil in a pot and fry the croquettes in it until they are golden brown.