Add cream, milk, sugar, salt, and cocoa to a saucepan and whisk while heating on medium high.
When the milk is simmering, reduce heat to low and add chocolate. Gently stir until chocolate has melted, remove from heat, and add vanilla.
Pour the milk mixture into an airtight container and refrigerate for at least three hours or overnight.
Freeze ice cream in an ice cream machine as per the manufacturer's instructions.
Scoop the churned dessert into a container and freeze for at least three hours or until hardened.