Put the coconut milk, double cream and coconut cream in a saucepan and bring almost to the boil. Meanwhile, whisk the sugar and the egg yolks in a bowl until thick. Pour the coconut milk mixture in a slow stream over the egg yolks and sugar, whisking constantly.
Rinse out the saucepan and return to a low heat. Pour in the custard mixture and stir in the desiccated coconut. Continue to stir constantly for 5-10 mins until the custard thickens slightly and you can trace a line through it with a wooden spoon. Pour into a bowl, then cover the surface of the custard with cling film, allow to cool, then chill for 30 mins.
Transfer the chilled custard to an ice cream maker and freeze according to the manufacturer’s instructions. Alternatively, transfer the mixture to a small freezable container with a lid and freeze for 1 hr, then use a fork or electric whisk to really churn through the ice cream to break up the ice crystals so that the mixture is the same consistency. Pop it back into the freezer for another 2-3 hrs, whisking it about every half hour, then cover the surface with a sheet of cling film and freeze with the lid on until as firm as ice cream. Take out of the freezer 10 mins before serving so it’s easy to scoop.