1. Slice eggs in half lengthwise, and carefully remove yolks, keeping egg whites intact.
2. Grate egg yolks using small holes of a box grater. Mash together yolks, mayonnaise, and next 3 ingredients. Add hot sauce, if desired. Stir ham and Swiss cheese into yolk mixture.
3. Spoon or pipe yolk mixture into egg white halves. Top with desired amount of toasted breadcrumbs.