Stir coffee, sugar, cardamom and 500ml water in a saucepan over medium heat until sugar dissolves, remove from heat, cool. Pour into a shallow tray, freeze until half frozen (1-1½ hours). Remove from freezer, break mixture into small ice flakes with a fork, then freeze again until just frozen (1-2 hours). Stir once more with a fork, breaking mixture into ice flakes.
Whisk cream and icing sugar in a bowl until soft peaks form and refrigerate until required.
Process pistachios in a food processor until finely ground. To serve, divide granita among chilled glasses, top with cream, scatter with ground pistachios and serve immediately.