In a medium pan, measure in the sweetener and then add the tinned coconut milk. Heat gently until combined.
Add the cornflour to the dairy-free milk and stir until smooth. Add to the saucepan with the salt and stir until thickened.
Pour into a freezer-proof container and cool to room temperature, stirring every so often to prevent a skin forming.
For ice cream makers: chill and follow manufacturers instructions.
Without an ice cream maker. Place in the freezer, whisking every couple of hours with a fork to break up the ice crystals. Or pour straight into ice lolly moulds.