Preheat your oven to 350°F (175°C) and grease a 9x9-inch baking pan with parchment paper.
In a microwave-safe bowl, melt the butter and sugar together. Stir until smooth and glossy. Let it cool slightly before adding eggs, one at a time, stirring well after each addition.
Stir in cocoa powder, flour, baking powder, salt, and vanilla extract until just combined. Fold in chocolate chips if desired.
Pour the batter into the prepared pan and bake for 20-25 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Allow the brownies to cool completely before preparing the frosting.
In a medium bowl, beat together the butter, powdered sugar, cocoa powder, vanilla extract, and milk until smooth and creamy. Spread the frosting evenly over the cooled brownies.
Slice into squares and serve!
Notes
Feel free to experiment with frosting flavors like cream cheese, peanut butter, or mint to add your own twist to these brownies.