Using an espresso machine, use 1 3/4 cups strong espresso.
Alternatively, make 1 3/4 cups espresso using a French press or drip coffee maker.
Add the 1/4 cup sugar and stir until dissolved.
Taste the espresso and add more sugar if necessary.
Chill in the refrigerator, or, to hasten the process, pour the espresso into a stainless-steel bowl, set it in a larger bowl filled with ice, and stir the coffee until cold.
Pour the chilled coffee into two 9-by-9-inch stainless-steel pans.
Freeze for 15 minutes.
Stir well and return the pans to the freezer.
Continue freezing, stirring every 10 minutes, until the granita is completely frozen, about 40 minutes in all.
In a medium bowl, using a hand-held electric mixer, beat the cream with the remaining 4 teaspoons of sugar until the cream holds soft peaks when the beaters are lifted.
Scoop the granita into chilled serving bowls and top with the whipped cream.
