Preheat the oven to 375 degrees F (190 degrees C).
Combine brown sugar and butter in a bowl; beat until creamy. Beat in egg. Mix in flour, 1/2 of the chopped chocolate, cocoa powder, and baking powder until dough comes together.
Drop spoonfuls of the dough onto a cookie sheet, allowing enough room for the cookies to spread. Flatten slightly.
Bake in the preheated oven until edges are done but tops are a bit gooey, about 5 minutes.
Remove from the oven. Push remaining chocolate and mini marshmallows into the tops. Continue baking until tops are set, about 5 minutes more. Be careful to remove cookies before marshmallows burn.