Combine first 4 ingredients in a saucepan. Bring to a boil, and cook over medium-high heat 1 minute or until sugar dissolves, stirring constantly. Remove from heat; cool. Pour mixture into a 13 x 9-inch baking dish; cover and freeze at least 8 hours or until firm.
Remove mixture from freezer; scrape entire mixture with tines of a fork until fluffy. Store remaining granita in a container; cover and freeze up to 1 month. Garnish with a pirouette cookie and a mint sprig, if desired.