Preheat your oven to 350°F (175°C). Prepare a 9x13-inch rectangular baking dish by greasing it and lining it with parchment paper for easy removal.
In a large mixing bowl, whisk together the warm melted butter and granulated sugar until well blended.
Add the eggs individually, mixing thoroughly after each addition, then stir in the vanilla extract.
In a separate bowl, sift together the cocoa powder, all-purpose flour, baking powder, and salt. Gently fold this dry mixture into the wet ingredients until just incorporated—avoid overmixing.
Transfer the brownie batter into the prepared pan, spreading it into an even layer. Bake in the center of the oven for 28 to 32 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs attached. Allow the brownies to cool completely in the pan.
To prepare the coconut filling, combine the sweetened shredded coconut, sweetened condensed milk, and vanilla extract in a medium bowl. Stir until fully blended and thick.
Evenly distribute this coconut mixture across the cooled brownie layer, pressing it gently into place.
Sprinkle the mini marshmallows uniformly across the surface of the coconut layer. Place the pan under the oven broiler for 1 to 2 minutes, just until the marshmallows puff up and gain a light golden hue. Keep a close eye to prevent scorching.
Allow the marshmallow layer to cool slightly before proceeding.
In a microwave-safe bowl, melt the semi-sweet chocolate chips together with the butter in short 20-second bursts, stirring between each interval until smooth and glossy.
Pour the melted chocolate mixture over the marshmallow layer, using a spatula to spread it evenly to the edges.
Place the entire pan in the refrigerator for no less than one hour, or until the chocolate topping is fully set.
Once chilled, slice into neat squares using a sharp knife, cleaning the blade between cuts for a polished presentation.