Heat a grill pan or griddle on medium. Add one slice of bread and spread the tapenade over it. Layer the prosciutto on top, followed by the parmesan.
Cover with the other slice of bread. After the sandwich has cooked for about 3-4 minutes, flip to the other side. Cook for another 3 minutes and then take out of the pan. Add the arugula and drizzle of vinegar to the sandwich.