Place romaine on a platter and toss with parsley tops. Wrap hearts of palm in prosciutto and cut into bite size pieces on an angle. Arrange prosciutto wrapped palm sections and quartered artichoke hearts over romaine greens. Shred cheese with a vegetable peeler into short ribbons, working over the salad plate. Drizzle the salad with balsamic vinegar and oil; season with salt and pepper.