Pour the cream and coconut milk in a saucepan on a medium heat. Do not let it boil but heat it for about 3-5 minutes.
As the cream is heating, whisk the eggs and erythritol together.
Remove the cream from the heat and gently pour into the egg mixture. Whisk until combined.
Using a blender (hand or upright) blitz the strawberries, lemon juice and basil together until smooth (the odd chunk won’t hurt).
Add the strawberry mixture to the cream and stir thoroughly.
Pour this mixture back into the saucepan on a medium heat and whisk for 5 to 10 minutes until the mixture starts to thicken slightly.
Remove from the heat.
Add the vodka and stir (optional).
Allow to cool or place in the fridge for faster cooling.
Pour into the canister of an ice-cream maker and churn according to manufacturer’s directions. If you don’t have an ice cream maker, place in the freezer. Remove every 30 minutes to stir to distribute the ice crystals until frozen consistency is obtained. Can take about 4-5 hours.