Preheat the oven according to the cake mix package directions. Grease a 9x13-inch baking dish.
Stir together the graham cracker crumbs, brown sugar, and melted butter. Press the mixture evenly into the prepared baking dish.
Bake the crust for 10 minutes. Remove from the oven.
Prepare the chocolate cake batter according to the package directions.
Pour the batter over the baked crust and bake according to the package directions for a 9x13-inch pan.
Let the cake cool completely.
Use the handle of a wooden spoon to poke holes across the top of the cake.
In a large bowl, stir together the whipped topping and marshmallow creme until smooth.
Transfer about half of the mixture to a piping bag and pipe it into the holes in the cake.
Spread the remaining marshmallow mixture evenly over the top of the cake.
Refrigerate for at least 1 hour.
Sprinkle the mini marshmallows, chocolate pieces, and graham cracker pieces over the cake.
Broil for 30 seconds to 2 minutes, watching closely, until the marshmallows are toasted.
Serve immediately or refrigerate until ready to serve.