In a bowl, combine 3 tablespoons of the coconut milk with the cornflour to make a paste.
Put the remaining coconut milk in a pan with the coconut cream and agave syrup. Slowly bring to a simmer, then stir in the cornflour paste and salt. Bring the mixture to the boil, stirring constantly until slightly thickened, then remove from the heat and stir through the desiccated coconut. Cover and chill overnight, or if you don’t have time at least for 2 hours.
Pour into an ice cream machine* and churn according to the manufacture’s instructions or until the blade stops, about 45 minutes.
Spoon the soft ice cream into an airtight, freezable container and continue to freeze for at least 4 hours or overnight, until firm. Allow the ice cream to soften for 5–10 minutes until scooping. Serve with toasted coconut flakes, if using.
* Freezing ice cream without a machine: Pour the mixture into a shallow, wide, freezer proof container and freeze for 1 hour, until the mixture freezes, forming a border around the edge. Break up the ice crystals with a fork or whisk and return to the freezer. Repeat this whisking every 30 minutes or so, until evenly set and too thick to fork. It should take 2–3 hours.