Step 1: Preheat your oven to 350°F (175°C). Prepare a 9x13-inch baking pan by greasing and flouring it, or lining it with parchment paper, leaving an overhang on the sides for easy lifting.
Step 2: In a large mixing bowl, combine melted butter and granulated sugar. Stir well until combined. Add the eggs one at a time, mixing well after each addition. Finally, stir in the vanilla extract and the cooled brewed coffee.
Step 3: In a separate, medium-sized bowl, whisk together the flour, cocoa powder, salt, and baking powder. Whisking ensures even distribution of ingredients.
Step 4: Gradually fold the dry ingredients into the wet ingredients. Mix just until everything is combined; do not overmix. Pour the batter into your prepared pan, spreading it evenly.
Step 5: Bake for about 25-30 minutes. The brownies are done when a toothpick inserted into the center comes out mostly clean, with a few moist crumbs clinging to it. Once baked, let them cool completely in the pan on a wire rack.
Step 6: While your brownies are cooling, prepare the frosting. In a bowl, combine powdered sugar, softened butter, brewed coffee, and vanilla extract. Beat them together until you have a smooth, creamy frosting. If desired, add the heavy cream, a tablespoon at a time, until you reach your desired silky consistency.
Step 7: Ensure your brownies are completely cool before you spread the delicious coffee frosting over the top. If they're even slightly warm, the frosting will melt.
Step 8: Once frosted, slice your brownies into perfect squares and enjoy!