Add the beer to a small saucepan and boil until it reduces to 1/3 cup. It will take about 20 minutes. Keep an eye on it to prevent it from boiling over.
Preheat the oven to 325°F and line a loaf pan with parchment paper.
In a microwave-safe bowl, combine the butter, cocoa powder, sugar, and unsweetened chocolate. Microwave on full powder for 30 seconds. Stir, then microwave for another 30 seconds. Let the mixture cool for 1 minute.
Stir in 4 tablespoons of the beer concentrate, the egg white, vanilla, and salt.
Finally, mix in the flour and stir for 50 strokes to incorporate and activate the gluten in the flour.
Pour the mixture into the loaf pan and bake for 40-45 minutes. It’s done when the surface is dry and an inserted toothpick has only moist crumbs sticking to it. Let cool.
Once the brownies are cool, make the frosting. Beat together the softened butter and powdered sugar until combined. Beat in the remaining beer concentrate (1 tablespoon).