Preheat oven to 350 degrees F and line a baking sheet with parchment paper. Set aside.
In a mixing bowl, cream butter and sugar until light and fluffy, scraping down the sides of the bowl for about 3-5 minutes. Add eggs, butter and half and half and beat well.
Beat in flour, hot cocoa and baking soda just until combined. Stir in ½ cup mini chocolate chips.
Drop by rounded teaspoons onto a baking sheet. Bake for 7 minutes and remove from oven. Press 3 mini marshmallows into each cookie and return to oven. Bake for an additional 2 minutes. Remove from oven and let set for 1 minute before moving to a cooling rack to cool completely.
Once cookies are cook, place ¼ cup of mini chocolate chips into the corner of a small sandwich bag. Microwave on high, for about 70-90 seconds, checking every 20 seconds and kneading chocolate until it is melted.
Snip the corner of the bag and pipe chocolate onto each cookie. Let set to harden before serving.