If chilling longer than one hour, remove the dough from the fridge 30 minutes before baking. Preheat the oven to 350 F, line three baking sheets with parchment paper. Scoop the dough and roll it into ping pong ball sized dough balls, place at least 2 inches apart on prepared baking sheets.
Bake the cookies for 6 minutes, then remove from the oven and press the marshmallow cut side down in the center of the cookie. Return to the oven and bake an additional 3-4 minutes, until the marshmallows are softened. Allow the cookies to cool completely.
For the frosting: Add the heavy cream, butter, and cocoa powder to a small saucepan over low heat and stir until butter has melted and the mixture is smooth.