Place the sugar and water in a saucepan and bring to a simmer to dissolve the sugar. Once the sugar has dissolved, remove from the heat and set aside to cool.

Cut the melons in half through the ‘waist’ and scoop out the seeds and discard them, then scoop out most of the flesh into the bowl of a food processor.

Leave a wall of flesh inside the melon, about 1 cm (½ in) thick (so not scooping out right to the skin). Blend the flesh, adding the cool sugar syrup and the lime juice and zest. Reserve the hollowed-out melons, because these will be used as bowls for the granita.

Pour the blended melon into a container or baking dish that will fit in the freezer.

Place the four cantaloupe shells in the freezer too. Freeze for 1 hour, then use a fork to scrape the granita mixture. Freeze again and then scrape again. Repeat this two or three times until you have a granita texture.