How to Make It
In a large saucepan, combine the pineapple juice with the sugar, mint sprigs, coarsely chopped chile and a pinch of salt. Simmer over moderately high heat, stirring, until the sugar has dissolved, about 2 minutes. Remove from the heat and let stand for 30 minutes to cool slightly.
Strain the pineapple juice into a 9-by-13-inch glass baking dish. Stir in the chopped mint and the minced chile. Freeze until the mixture is icy around the edges, about 1 hour. Using a fork, scrape the icy shards into the center. Continue to freeze, stirring occasionally, until icy throughout, about 3 hours longer. Scoop the granita into bowls and serve.