In a medium sized saucepan, heat butter over medium heat until melted.
Once melted, lower heat to medium-low and add chocolate chips. Stir continuously until melted. Set aside and let melted chocolate cool.
In a medium sized bowl, mix together flour, cocoa powder, baking powder, baking soda, and salt. Set aside.
In a large bowl, using a hand mixer, beat eggs and sugar. Add in vanilla.
Pour cooled chocolate into wet mixture and beat until all combined.
Slowly add in flour mixture until dough is formed and everything is combined.
Let dough chill 20 minutes in fridge. Do not let chill much longer as the dough will dry out.
Preheat oven to 350F and line baking sheet with parchment paper.
Roll about 2 tbsp of dough into balls and bake for 10 minutes, then add half a marshmallow to the top of each cookie. Bake another 2-3 minutes. Let cool.
Make icing by mixing together all the ingredients. Drizzle over the cooled cookies and top with sprinkles.