In a medium saucepan, melt the butter and 6 oz. chopped chocolate, stirring frequently, over medium heat. Set aside.
Using a stand mixer fitted with the paddle attachment (or a large mixing bowl with a hand mixer), combine the brown sugar, eggs and vanilla extract and beat on medium speed until smooth and creamy. Add the chocolate mixture and beat until just combined.
In a separate bowl, combine the flour, cocoa powder, baking powder and salt. Mix well. Gradually add to the batter and beat on medium speed until just combined. Wrap the dough in plastic wrap and refrigerate for a minimum of 1 hour.
Preheat oven to 325 degrees F. Line 3 large baking sheets with parchment paper. Using a tablespoon, scoop the dough and roll between your palms to form 1-inch balls. Arrange the balls 2 inches apart on each cookie sheet, flattening slightly using fingers. Bake until the tops of the cookies begin to crinkle, 10-11 minutes.
Gently press one square of baking chocolate into the center of each cookie, followed by a marshmallow half. Bake for an additional 3-4 minutes, or until marshmallows are soft and puffy. Top with grated chocolate.