The coarse crystals in this sweet and slightly spicy granita distinguishes it from other frozen desserts.
Pulse ginger in a food processor until finely chopped. Transfer ginger to a large saucepan. Add plums, sugar, salt, and 5 cups water. Bring to a boil over medium-high heat. Reduce heat to medium. Simmer, stirring occasionally, until sugar has dissolved and plums have broken down, about 15 minutes.
Pour plum mixture through a fine sieve into a 9-by-13-inch shallow nonreactive dish; discard solids. Stir in vanilla. Chill in freezer until edges are frozen, about 1 1/2 hours. Remove from freezer; scrape with fork tines, pulling from edges into center. Return to freezer. Repeat process every 30 minutes until mixture is the texture of shaved ice, about 4 1/2hours. Spoon into serving bowls, and garnish with plums.
For the right texture, scrape the granitas every half hour for 4 1/2 hours. Same-day preparation is best -- after too long the consistency will change from light and layered to overly dense.