Cut the melon flesh into 1-inch cubes. Reserve a quarter of the cubes and put the rest into a blender or food processor fitted with a purée blade. Add the coconut milk and lime juice/zest and purée until smooth. Add the peppers, ginger, and salt. Pulse a few times. Add the basil and mint and pulse a few more times. Add the remaining chunks of melon, but do not pulse.
Chill the soup for 1 hour in the fridge. Serve in beautiful, clear wine glasses that have frosted up in the freezer for that hour. Garnish with the reserved basil and mint sprigs. For extra sass, place the glasses on a small plate with a festive napkin under the stem.