Rinse the fennel and remove the hard stalk. Remove the fennel fronds, finely chop, and set aside. Remove the stalks, and cut the fennel into paper-thin slices. Separate the shaved pieces of fennel by hand. Mix the vinegar with the oil, then season to taste with salt and pepper. Mix the fennel with the dressing, then toss to combine. Set aside and let infuse for 1 hour. Cut the ham into very fine strips.
Mix the ham and the fennel fronds with the marinated fennel. Season to taste with salt and pepper, sprinkle with the parmesan cheese, and serve.