Pour the coffee into a jug and stir in the sugar until it has dissolved. Add the coffee liqueur and leave to cool completely.
Once cold, pour the mixture into a freezable container and put in the freezer for 1 hr. Mix it with a fork – you should start to see ice crystals forming at the edges. Return to the freezer for 20 mins then stir again. Repeat once or twice more until the granita is all clumps of ice.
Serve in glasses or bowls as an elegant dessert. For a more indulgent version, add a dollop of mascarpone and a grating of dark chocolate.