Place the butter and chopped chocolate in a heat safe bowl, and microwave at 30 second intervals, stirring frequently until chocolate is melted and mixture is smooth.
Cool for 15 minutes.
In a medium bowl, whisk together the flour, cocoa powder, baking powder and salt.
In a mixer, beat the sugar, eggs and vanilla on low speed until smooth.
Stir in the cooled chocolate mixture just until blended.
Add the flour mixture in 2 batches, mixing until just combined.
Cover and chill the dough for at least 1 hour.
Preheat the oven to 325 degrees. Line 2 baking sheets with parchment.
Scoop tablespoons of dough and roll into balls. Place 2-3 inches apart.
Bake until the tops of the cookies crack, about 10 to 12 minutes.
While cookies are baking, cut the marshmallows in half and place a square of chocolate on the cut side of each marshmallow. Set aside.
Remove the cookie sheets from the oven; gently press a marshmallow half, chocolate side down, into each cookie. Bake until the marshmallows start to soften, about 4 minutes.
Remove from oven and let cool for about 5 minutes. Garnish tops with grated chocolate and cool on racks.
Repeat, using fresh parchment with each batch to prevent sticking.