In a medium saucepan over low heat, melt the semisweet chocolate and butter together until smooth. Set aside to cool slightly.
Meanwhile, in a large bowl, whisk together the flour, granulated sugar, brown sugar, cocoa powder, baking soda, and salt.
Mix in the eggs and vanilla extract into the pot with the melted chocolate mixture, then pour the chocolate mixture into the dry ingredients and stir until a dough forms. Mix in the chocolate chips. Wrap the bowl with plastic wrap and allow it to chill for 1 hour.
If chilling longer than one hour, remove the dough from the fridge 30 minutes before baking to make it soft enough to work with. 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 cooca powder to a small saucepan over low heat and stir until butter has melted and the mixture is smooth. Add the powdered sugar to the pan and mix until completely combined. Allow to cool slightly then spoon a small amount over each cooled cookie.
Add sprinkles to the wet frosting, then allow the frosting to set for 15-20 minutes
Notes
Chilling is important - This cookie dough will be sticky and difficult to work with if you don't chill it before baking.
You can chill for longer than an hour - Up to a day ahead of time if needed. If you do this, let the dough sit out at room temperature for 30 minutes or so so that it gets soft enough to work with.
Try flavored marshmallows - Chocolate, peppermint, or cinnamon gourmet marshmallows would be delicious in these cookies!
Mini marshmallows worktoo- Use three of them on each cookie instead of half of a full-sized marshmallow.
Let the cookies cool before frosting - If they are too warm, the frosting will slide right off.
To Store: Keep your cookies in an airtight container in a single layer for up to 3 days.