Dressing: Mix garlic, palm or brown sugar, fish sauce, lime juice, chiles, and lime leaves in a bowl. Roughly chop shrimp and peanuts by hand or in a food processor and add to garlic mixture. (The dressing can be made in advance and stored up to 3 days in the refrigerator.)
To serve, arrange each variety of melon cubes in alternating rows on a platter or in individual bowls. Spoon dressing over melon in a strip and garnish with cilantro. Serve chilled.
c.1997, M.S. Milliken & S. Feniger, all rights reserved