Whisk the coffee and sugar together in a large bowl or measuring cup, stirring until the sugar dissolves. Whisk in the cream, liqueur, vanilla and cinnamon until combined. Pour the mixture into a freezer-safe baking dish. Freeze for 2 hours, then bring it out and scrape the mixture with a fork. Continue to scrape the dessert every hour for 4 to 6 hours before serving.
Spoon the granitas into 4 glasses. You can add a few drizzles of liqueur to make it less icy and more boozy. Top with fresh whipped cream or marshmallow frosting and a sprinkle of dark cocoa powder and cinnamon.