Heat sugar and water in a saucepan stirring occasionally until the sugar dissolves. Boil for 10 minutes without stirring. Remove it from the heat and allow to cool slightly. Mix the cooled syrup with the coconut milk and pour into a container. Cover and freeze for about 3 hours or until semi-frozen around the edges and mushy in the centre.
Transfer the mixture to a bowl and cut up with a knife. Then place half the quantity at a time in a food processor and process until smooth, or whisk thoroughly by hand. Turn the mixture into a bowl. Whip the cream until soft peaks form and fold into the ice-cream, then stir in the desiccated coconut. Return the mixture to the container and freeze again until solid.