To make a traditional Cuban sandwich without pork, substitute chicken, turkey or beef for pork when making the sandwich. Cuban sandwiches are traditionally served with Swiss cheese, pickles and mustard.
To make a Cuban sandwich with chicken, marinate four boneless, skinless chicken breasts in a combination of mayonnaise, mustard, lime, garlic, salt and pepper. Cook the chicken breasts on a grill set to medium heat, and assemble the sandwiches by layering turkey ham, sliced chicken breast, Swiss cheese and sauce on a soft roll. Grill the entire sandwich until it is heated through.
To make a Cuban sandwich with turkey, split a loaf of French bread in half, and spread mustard on the top half of the bread. Layer pre-cooked turkey ham, pre-cooked turkey breast and Swiss cheese on the bottom of the bread, and cover the sandwich with the top piece of bread. Cut the sandwich into four pieces, and heat 1 tablespoon of butter in a skillet on medium-high heat. Heat the sandwich in the skillet, flipping once, until it is heated through.
To make a Cuban sandwich with beef, marinate flank teak in a combination of cilantro, olive oil, basil, parsley, lime juice and salt, and cook the flank steak on a grill pan until it is medium-rare. Slice the flank steak, and serve it with browned onions on toasted ciabatta bread.