Preheat your oven to 350°F (175°C). This ensures that your brownies bake evenly.
Line a 9x13-inch baking pan with parchment paper, leaving some overhang on the sides. This will help you lift the brownies out easily once they’re cool.
In a saucepan over medium heat, melt the unsalted butter. Remove from heat and let cool slightly.
In a large mixing bowl, combine the melted butter, granulated sugar, and brown sugar. Stir until well combined. Add the eggs, one at a time, mixing well after each addition. Finally, stir in the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, stirring until just combined. Be careful not to over-mix.
Pour the brownie batter into the prepared baking pan and spread it evenly. Bake in the preheated oven for about 25-30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Remove the brownies from the oven and immediately sprinkle the miniature marshmallows evenly over the top. Return the brownies to the oven for an additional 5-7 minutes, until the marshmallows are puffed and slightly golden.
While the brownies cool, prepare the chocolate glaze. In a double boiler or microwave, melt the semi-sweet chocolate chips with the milk until smooth. Stir in the powdered sugar and mix until well combined.
Once the marshmallows have cooled slightly, pour the chocolate glaze over the top of the marshmallows, spreading it evenly.
Allow the brownies to cool completely in the pan. Once cooled, use the parchment paper to lift them out, then cut into squares. Serve and enjoy your delicious Mississippi Mud Brownies!