Preheat the oven to 350º (180ºC). Line 2 large cookie sheets with parchment paper.
In a medium-sized bowl, sift together the flour, cocoa powder, baking powder, baking soda, and salt until well blended.
In a large bowl, beat the butter, granulated sugar and brown sugar with an electric mixer at medium speed, until pale and fluffy. Mix in the eggs and the vanilla in 3 separate additions, making sure each addition is incorporated before adding the next. On low speed, mix in the flour mixture in 2 additions, just until combined.
Roll the fudge filling into tablespoon-sized balls.
Roll the cookie dough into 2-tablespoon-sized balls then flatten them into disks. Place a ball of fudge filling in the middle of each disk. Wrap the cookie dough around the ball of filling, sealing it completely.
Place the cookies about 2 inches apart onto the prepared baking sheets. Bake until the tops of the cookies are set, about 9-11 minutes. Remove from oven.
Turn on the broiler. Place a marshmallow on top of each cookie.
Broil the cookies until the marshmallows are toasted. This takes about 1 minute. CAUTION: Watch the cookies carefully when broiling. They can go from done to burnt in the blink of an eye!