Cut mango into 1/4- to 1/2-inch slices (about 16). Place 1 mango slice on top of 3 arugula leaves and 1 to 2 basil leaves.
Cut each prosciutto slice lengthwise into 4 strips. Wrap center of each mango bundle with 1 prosciutto strip. Arrange on a serving platter, and sprinkle with pepper.
To make ahead, prepare recipe as directed. Cover bites with damp paper towels, and chill 30 minutes.
Notes
Ask for paper-thin slices of meat at the deli counter. To ease prep, look for a package of presliced mango in the produce section. We do not recommend jarred mango slices—they're too soft.