Trim rind from melon. Cut in half; discard seeds. Slice melon into small wedges, then cut each slice into small cubes.
Place melon in bowl. Drain bocconcini, then add to bowl along with oil and dip mix. Toss to evenly coat.
Cut prosciutto slices in half cross-wise. Roll up or fold pieces in half; place on a platter. Scatter melon and cheese over top. Garnish with basil, if desired.