Put all ingredients except lime zest in a pot and bring to a boil. Strain and pour into shallow pan. Place in freezer and every twenty minutes stir with a fork until ice crystals form and it is nice and fluffy. Candied lime zest: Cover the zest with cold water and bring to a boil. Strain zest and repeat process 3 times. After the fourth time add 1 cup water and 1/2 cup sugar and cook slowly until zest is soft. Remove zest to parchment paper and cool. Use as a garnish for the granita.
Recipe courtesy of Deb Racicot, Picholine Restaurant, New York, NY