This icy treat makes the most of rich ripe watermelon. Melons can vary in flavor quite a bit, so taste the mixture before freezing and add more honey or lime if desired.
Place half of the watermelon in the bowl of a food processor and process until smooth. Pour into a 9-by-13-inch glass baking dish. Add the remaining watermelon to the processor along with the honey and lime juice and process until smooth.
Pour into the baking dish, stir until combined, and place uncovered in the freezer. Freeze until ice begins to form around the edges of the pan, about 30 minutes. Rake with a fork to break up large ice clumps, return to the freezer, and continue stirring about every 30 minutes until all liquid is crystalized, about 3 hours total.
Using a large fork, flake the granita into bowls or into an airtight container to freeze up to 1 week. Serve garnished with mint or basil, if desired.