Trim ends of zucchini and discard. Using a vegetable peeler, slice zucchini lengthwise into 16 paper-thin slices; place in a single layer on a work surface. (Discard first slice of peel and seedy center.) Wrap and chill remaining zucchini for another use.
Stack ham slices and cut into 4 long strips. Repeat with cheese slices.
Sprinkle zucchini slices with pepper.
Lay a ham strip in center of a zucchini slice and top with a cheese strip. Starting at one end of zucchini strip, roll it into a tight spiral; secure with a toothpick. Repeat.
