This icy treat is the perfect way to end a leisurely summer meal or to refresh yourself on a hot afternoon.
Add 2 cups sugar to espresso or coffee while it is hot. Stir to dissolve, and let cool to room temperature.
Choose a metal or freezerproof glass pan that will fit easily into your freezer (a 9-by-12-by-3-inch pan works well). Pour cooled espresso into pan and place in freezer.
When edges begin to freeze, after about 30 minutes, stir with a fork and replace in freezer. Stir again about every half hour until large crystals begin to form and mixture is more solid than liquid; then stir more frequently, about every 15 minutes. The total freezing time will be anywhere from 2 to 6 hours, depending on your freezer. Finished granita should resemble shaved ice, with no liquid visible on the bottom.
Whip cream with vanilla and remaining 1 tablespoon sugar until soft peaks form. Layer granita with the cream in chilled glasses and serve immediately.
Finished frozen granita can be stored, covered, in the freezer overnight. If granita solidifies, scrape and chop up with a metal spatula before spooning into serving glasses.