In a small saucepan stir sugar and 3/4 cup water over medium until sugar dissolves. Stir in pepper. Let stand, covered, 30 minutes.

Meanwhile, puree melon and cilantro in a blender or food processor, in batches if necessary. Transfer to a 1 1/2- to 2-quart baking dish. Strain syrup into puree; stir to combine. Freeze, covered, 3 to 4 hours or until frozen. Using a fork, break mixture into slushy chunks. This allows coarse ice crystals to form. Freeze 1 to 2 hours more or until solid again. Use a fork to scrape the frozen surface into fine icy shards. It will look like shaved ice. (For an airier, almost creamy texture, process frozen mixture in a food processor 1 minute or until smooth. Freeze at least 1 hour more before serving.)

Serve sprinkled with chile-lime seasoning. Makes 4 cups.