In a medium-sized saucepan, combine the heavy cream, whole milk, granulated sugar, unsweetened cocoa powder, and salt. Stir the mixture until the sugar and cocoa powder have dissolved completely.
Heat the mixture over medium heat, stirring occasionally, until it starts to steam. Do not let it boil.
Once the mixture has started steaming, remove it from the heat and add the mini marshmallows. Stir until the marshmallows have melted completely.
Stir in the vanilla extract and let the mixture cool to room temperature.
Once the mixture has cooled, transfer it to an ice cream maker and churn according to the manufacturer’s instructions.
Once the ice cream has finished churning, transfer it to a freezer-safe container and freeze for at least 2 hours or until it reaches the desired consistency.