Combine the water, sugar, and jalapeño in a small saucepan and cook over medium-high heat, stirring frequently. When the mixture comes to a boil, lower heat and simmer for 5 minutes more.
Cool mixture to room temperature and then strain through a fine-mesh sieve.
Add pineapple, lime juice, salt, and sugar mixture to a food processor and process until smooth.
Pour mixture into 9 x 13 inch baking pan. Freeze until ice forms around the edges. Stir with a fork and return to the freezer—repeat every 20–30 minutes until granita is completely frozen.
Use a fork to scape the granita into fluffy crystals and serve.
Notes
Cook time is the time in the freezer. Freeze time is approximate—it takes about 3 hours in mine.
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