In a medium saucepan (or in a microwave safe bowl, using 50% power), melt the butter and chocolate, stirring frequently. Once melted, set aside to cool slightly.
In a medium bowl, whisk together the flour, cocoa powder, baking powder and salt.
In the bowl of an electric mixer, beat the sugar, eggs and vanilla on low speed until well combined.
Add the cooled chocolate mixture and blend until just combined.
While mixing, add the flour mixture slowly and blend until just combined.
Scrape down the sides of the bowl, then cover the dough and refrigerate at least 1 hour. The dough should be firm. If making the dough a day ahead, let sit at room temperature for 30 minutes before shaping.
Preheat oven to 325*F. and line 2 baking sheets with parchment paper or a silpat type liner. Use a tablespoon (or a tablespoon sized cookie scoop) to scoop the dough, then roll the dough in your hands to create balls. Arrange the balls about 2 inches apart on your baking sheets, then flatten slightly.
Bake cookies about 12 minutes.
While the cookies bake, cut the large marshmallows in half (crosswise). When the cookies have baked, remove from oven and press one marshmallow half (cut side down) into the center of each cookie. Return the cookies to the oven and bake another 2-3 minutes. Allow the pan of cookies to cool a few minutes, then transfer cookies to cooling rack.
Prepare cookie icing
Prepare cookie icingby combining all ingredients in a medium bowl and mixing together with a whisk. Place wire cooling rack (with cookies on it) over a baking sheet (to catch any excess icing). Spoon a small amount of icing onto the top of each marshmallow, and use the back of the spoon to spread it a bit. After icing just a couple cookies, top with sprinkles before the icing dries.
Allow icing to set up about 30 minutes before serving.
Cookies can be stored in an airtight container up to 2 days. Change the sprinkles to coordinate with various holidays.