Bring the water to a boil in a nonreactive saucepan with a tight-fitting lid. Remove from the heat, whisk in the espresso, cover and allow to steep for 10 minutes. Strain once to eliminate most of the grounds, then strain through a coffee filter or dampened napkin or paper towel to eliminate all the remaining grounds. Measure the coffee: there should be 3 cups. If not, add water to make 3 cups. Stir in the sugar until it is dissolved and cool to room temperature.
Pour the mixture into a nonreactive gratin dish or roasting pan and place in the freezer. When the mixture starts to freeze, stir it every 10 minutes, scraping the granita off the bottom and sides of the pan so that it freezes evenly. When the granita no longer has any unfrozen liquid in it, stir well and pack in a chilled container. Press plastic wrap against the surface, cover the container with a lid, and store in the freezer. The granita is best on the day it is made. Serve the granita in chilled stemmed glasses with a spoonful of unsweetened whipped cream.
If the granita freezes to a solid block, pop it out of the container, cut into thick slices with a stainless steel knife, and chop the slices finely. Replace in the container and freeze until serving time.
© 1990 Nick Malgieri. All rights reserved.