Mix cinnamon and sugar into coffee until the sugar dissolves, then stir in the rum.
Pour the mixture into a non-stick jelly roll pan or a flat baking sheet and place in the freezer to chill.
After an hour, when the mixture begins to look slushy, begin scraping it from the edges using a spatula.
Repeat every 30 minutes or so until the mixture is the desired texture. Using a spoon or spatula, scoop the granita into tumblers.
Top with fresh whipped cream and a sprinkle of cinnamon. Serve with a straw or dessert spoon.