Put the picked over and washed fruit in a saucepan with the sugar and three or four tablespoons of water.  Set the pan over a low heat and gently stew the blackcurrants until they are soft.

Purée them, (this is easiest in a liquidiser or food processor)  then sieve out the pips and leave until cold.

Stir in the cream, and if you are using it, the crème de cassis.

Put in an ice cream maker if you have one. Alternatively, put in the freezer and stir with a fork occasionally until set.