Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking pan.

In a saucepan over medium heat, melt the butter. Remove from heat and stir in the sugar, mixing until well combined.

Allow the mixture to cool slightly, then stir in the eggs and vanilla extract, mixing until smooth.

In a separate bowl, whisk together the flour, cocoa powder, baking powder, and salt.

Gradually add the dry ingredients to the butter mixture, alternating with the brewed coffee, and stir until just combined.

Pour the batter into the prepared baking pan, spreading it evenly. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.

While the brownies are cooling, mix the powdered sugar, milk, and instant coffee granules together in a small bowl until smooth.

Once cooled, spread the frosting over the brownies. Allow to set for a few minutes before cutting into squares.