Reduce the Coffee: Pour the strong brewed coffee into a small saucepan and heat it over medium heat until it reaches a boil.
Concentrate the Coffee: Reduce the boiling coffee until only 2 Tablespoons remain, then remove the saucepan from the heat and set the concentrated coffee aside.
Prepare the Baking Pan: Preheat the oven to 350°F (177°C). Line an 8-inch or 9-inch square baking pan with foil, then spray the foil with nonstick spray. Set the prepared pan aside.
Melt the Chocolate Mixture: Place the sliced butter and coarsely chopped semi-sweet chocolate in a medium saucepan over medium heat. Stir frequently until the mixture is completely smooth.
Cool the Chocolate Mixture: Remove the melted chocolate mixture from the heat and allow it to cool for about 15 minutes.
Build the Brownie Batter: Whisk the light brown sugar and granulated sugar into the cooled chocolate mixture until combined. Add the eggs one at a time, whisking after each addition until smooth.
Add the Coffee: Whisk 1 Tablespoon of the concentrated coffee into the chocolate mixture until evenly incorporated.
Finish the Batter: Add the all-purpose flour and salt, then stir gently until the ingredients are completely combined.
Fill the Pan: Pour the finished brownie batter into the prepared square baking pan and spread it into an even layer.
Bake the Brownies: Bake at 350°F (177°C) for 25–30 minutes, or until a toothpick inserted into the center comes out mostly clean.
Cool Completely: Allow the brownies to cool completely in preparation for frosting.
Melt the Frosting Base: For the mocha frosting, place the chopped unsweetened baking chocolate and butter in a small saucepan over medium heat. Melt until smooth, then allow the mixture to cool for 15 minutes.
Combine the Frosting Ingredients: Transfer the cooled chocolate-butter mixture to a medium bowl, or use the bowl of a stand mixer fitted with the paddle attachment. Add the concentrated coffee and 1 Tablespoon of milk or cream to begin.
Add the Powdered Sugar: Turn the mixer to low speed and slowly add the powdered sugar. Increase the speed to medium and beat until the frosting is completely combined, scraping down the sides of the bowl as needed.
Adjust the Frosting: Add additional milk or cream, up to the remaining amount specified, as needed while mixing. Add a pinch of salt to taste.
Remove the Brownies: Once ready to frost, lift the foil overhang straight upward to remove the brownie block from the pan. Peel away the remaining foil and place the brownie block on a large cutting board or other safe-to-cut surface.
Frost the Brownies: Spread the mocha frosting evenly across the top of the completely cooled brownies.
Cut and Serve: Cut the frosted brownie block into 16 individual servings.
Store the Brownies: Keep leftover brownies at room temperature for up to 1 week. For longer storage, freeze the brownies for up to 3 months and thaw them in the refrigerator overnight.
