Start by heating the milk, sugar, and cocoa powder in a saucepan over medium heat. Stir constantly until the mixture becomes smooth and the sugar dissolves completely. This should take around 5 minutes. Once that’s done, remove it from the heat.

Stir in the heavy cream into the cocoa mixture, followed by the chopped semi-sweet chocolate. Continue to stir until the chocolate melts fully, and the mixture is smooth and velvety.

Now, let the chocolate cream mixture cool to room temperature. You can speed up this process by placing the saucepan in a bowl of ice water. While it’s cooling, add in the vanilla extract for an extra layer of flavor.

Once the mixture is at room temperature, pour it into your ice cream maker and churn according to the manufacturer's instructions. This typically takes about 20 minutes, but be sure to keep an eye on it so it reaches a thick, soft-serve consistency.

In the final stages of churning, add the mini marshmallows into the mix. They will soften and break up just slightly, creating pockets of gooey marshmallow goodness throughout the ice cream.

Transfer the churned ice cream into a storage container. Place the container in the freezer for at least 3-4 hours, or until it’s firm enough to scoop.