Rinse and dry the crayfish tails. Fry in hot oil for about 2 min on both sides, remove and cool.
Cut melons in half, scrape out seeds with a spoon. Using a ball cutter, cut out 16 balls and set aside. Remove remaining flesh with a spoon. Leave a rim about 2 cm thick. Finely mash flesh in clear soup. Season with juice of one lemon, salt and pepper. Leave to cool for about 30 minutes.
Cut the basil – except for a few leaves – into strips. Pour the soup into the melon cavities. Garnish with the crab tails, melon balls and basil. Serve the soup on ice cubes.