Preheat the oven to 350°F (175°C). Line an 8-inch square baking pan with parchment paper, leaving some overhang on the sides for easy removal.
Melt the butter and chopped semi-sweet chocolate together in a microwave-safe bowl in short intervals, stirring between each interval until completely smooth. Let the mixture cool slightly.
Whisk the granulated sugar and brown sugar into the melted chocolate mixture until well combined.
Add the eggs and vanilla extract. Whisk until the mixture is smooth, glossy, and fully incorporated.
In a separate bowl, whisk together the all-purpose flour, cocoa powder, espresso powder, baking powder, and salt.
Gradually add the dry ingredients to the chocolate mixture. Fold gently with a spatula just until no visible streaks of flour remain. Avoid overmixing.
Pour the brownie batter into the prepared pan and spread it evenly. Bake for 23–27 minutes, or until the center is set and a toothpick inserted into the center comes out with a few moist crumbs.
Place the pan on a wire rack and allow the brownies to cool completely before frosting.
Make the coffee frosting by beating the softened butter until creamy. Gradually add the powdered sugar and beat until smooth.
Add the espresso powder, heavy cream, vanilla extract, and salt. Beat until the frosting is light, creamy, and easy to spread.
Spread the coffee frosting evenly over the completely cooled brownies.
For cleaner slices, chill the frosted brownies briefly before cutting. Slice into 16 squares and serve.