Preheat the oven to 350ºF. For thick brownies, spray a 9x9" pan with non-stick spray or line with parchment paper. If you'd like to make thinner brownies, use a 9x13" pan.
Prepare the brownie mix according to the package directions. Then pour batter into the prepared pan. Bake for 30 minutes, or until almost done. Do not overcook. Remove from oven and then sprinkle marshmallows over the top so that they are covering the brownies in an even layer. Bake an additional 3 minutes, or until the marshmallows have puffed up. Remove from oven and allow to cool.
Make the frosting:
Combine the butter, powdered sugar, cocoa powder, milk and vanilla in a large bowl. Beat with electric beaters until smooth. Add more milk or powdered sugar if needed to reach a smooth and creamy frosting. Then place spoonfuls on top of the marshmallows once cooled. Gently spread evenly.
I like to cut the brownies in 5x4 rows with a plastic knife.
If you make in a 9x13" pan, you may want to double the frosting and use an extra cup of mini marshmallows. Make sure to use fresh marshmallows for optimal flavor. If you want to make these brownies even richer, add 1/2 cup chocolate chips in the brownie batter before baking.