This recipe is from "Without Reservations: How to Make Bold, Creative, Flavorful Food at Home," by Joey Altman (Wiley, $35). A fruity silver or white (clear) tequila, or an oak-aged, mellower añejo, will work well in this recipe.
1 cup sugar
2½ cups water
½ cup tequila
6 tablespoons fresh lime juice
¼ cup fresh orange juice
¼ cup Cointreau
Mint sprigs, for garnish
Heat the sugar with 2½ cups water, stirring until the sugar is completely dissolved. Remove from the heat and stir in the tequila, lime and orange juices, add Cointreau until well mixed.
Pour the mixture into a 13-by-9-inch glass baking pan or covered plastic container. Freeze until slushy, about three hours, then break up mixture by running tines of a fork through it several times. Repeat every two hours or so until the granita is icy throughout, about eight hours. At the end, you will have piles of fine slivers of ice. Pack the granita loosely in a covered plastic container and freeze for up to three days.
To serve, scoop granita into a martini glass and garnish with a sprig of mint.