Add the sugar to the freshly brewed coffee or espresso and stir until the sugar is dissolved. Then, add the cinnamon stick and let the coffee sit until it cools to room temperature.
When the coffee has cooled, remove the cinnamon stick and pour the coffee into a wide, shallow, freezer-safe dish. Put the dish in the freezer. After 45 minutes, take the dish out of the freezer and stir it with a fork. Return the dish to the freezer.
After 30 minutes, take the dish out of the freezer and stir with the fork again before returning the dish to the freezer.
Continue freezing the granita, stirring it with a fork every 30 minutes, until completely frozen, about 3 to 4 hours total.
Serve topped with whipped cream.