The day before you make the ice cream, refrigerate the ice cream maker basin according to manufacturer instructions.
When the machine is ready, empty the cold coconut milk, the sugar, the vanilla, the salt, and the blackberries into a blender. Blend till they are totally smooth (1-3 minutes).
Transfer the mixture to the ice cream maker. (If it's gotten hot while blending, you may wish to cool it down in the fridge first, but it wasn't necessary for me.) Allow the ice cream to churn for about 20-25 minutes, according to the machine instructions, until it's ready. Transfer the ice cream to a freezer-safe container and allow it to sit in the freezer for a few hours. Serve, garnished with mint if you like.