This dessert is as simple as it gets. There’s no cooking involved, just some patient freezing time to get the granita to the proper consistency. If you don’t like rosewater, you can leave it out, but do use vanilla extract in its place (orange blossom water also complements the melons well, if that’s more your speed).
Using a spoon, dig out bite-size chunks from both melons and let them fall into a bowl; discard the rinds. Weigh out 1 3/4 pounds of chunks (about 1/4 of the flesh) and place in a blender with the sugar, lime juice, salt and rosewater; place the remaining chunks in a bowl, cover and refrigerate until ready to use. Blend on high until the sugar dissolves and the puree is super smooth, at least 1 minute.
Pour the melon puree into a shallow glass dish and place in the freezer. Let the puree freeze for 1 hour, then stir with a fork to break up any frozen chunks, redistributing them in the puree. Repeat, stirring the puree every hour until it forms an icy granita, about 4 hours total. (You can do this a day ahead of time if you like.) Several minutes before you plan to serve the granita, place a large platter with a rim in the freezer or refrigerator to chill.
When ready to serve, arrange the chilled melon chunks on the chilled platter so they sit in more or less an even layer. Quickly spoon the granita all over the melon (use as much as you like and save the rest in the freezer), then sprinkle with some pistachios and edible flowers. Serve the granita at once, family-style, so people can spoon it into glasses or dig in with spoons directly from the platter.
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