1. Combine the water, sugar, and basil in a medium saucepan; bring to a boil over medium-high, stirring until the sugar dissolves completely. Remove from the heat, and cool to room temperature, about 30 minutes.
2. Pour the mixture through a fine wire-mesh strainer into a 13- x 9-inch baking dish; discard the basil leaves and stems. Stir in the lemon juice and, if desired, the vodka. Freeze until just beginning to harden, about 2 hours.
3. Scrape with a fork to form small crystals, and freeze until fully frozen, about 3 hours, scraping with a fork at 1-hour intervals. Serve the granita in chilled glasses, and garnish with the small basil leaves.