Preheat the oven to 350 degrees F. Line an 8” x 8” pan with parchment paper.
Whisk together the flour, cocoa powder, and salt in a medium bowl. Set aside.
Place the chocolate chips in a large, heat-proof bowl. Set aside.
In a small saucepan, melt the butter over medium heat. Simmer for 5 to 7 minutes, whisking often. The fat will begin to separate and then the butter will become foamy – Continue to cook while foaming, whisking constantly for 1 to 2 minutes, or until the butter is a deep amber color.
Pour the melted chocolate over the chocolate chips and whisk until smooth. Slowly pour the beer into the chocolate mixture and whisk until combined.
In a medium bowl, beat together the eggs, sugar, and vanilla for two minutes, scraping down the sides. Pour the egg mixture into the chocolate mixture and gently whisk just until combined.
Add the flour mixture to the egg and chocolate mixture. Gently whisk just until combined.
Pour the batter into the prepared pan and bake at 350 degrees F for 35 to 45 minutes, or until a toothpick comes out clean. Cool in the pan for five minutes. Transfer to a wire rack and let cool completely before frosting.
Mix the instant coffee or espresso together with the hot water until the coffee grounds have completely dissolved. Set in the refrigerator and let cool completely.
In a medium bowl, whisk together the powdered sugar and cocoa powder. Set aside.
In a large bowl, using a hand mixer or stand mixer, cream the butter, coffee, and vanilla together on medium speed for 2 minutes. Scraping down the sides halfway through.
Add the dry ingredients to the butter mixture and beat on medium speed until you get a frosting consistency, about 5 minutes. If the frosting is too dry, add milk, 1 tablespoon at a time. If the frosting is too wet, add powdered sugar, 1 tablespoon at a time until the desired consistency is reached.
Frost the cooled brownies, cut, and enjoy!