Preheat oven to 350 degrees F. Line a 9x13 rectangular baking pan with foil, extending the sides of the foil over the edges of the pan. Spray the foil liberally with cooking spray; set aside.
In a medium saucepan, add the beer and cook on medium-heat until reduced to about 3/4 cup. Remove from the heat and pour the beer concentrate into a separate bowl. Return the pan back to the stove and add in the butter and chopped chocolate; cook on medium-low, stirring constantly, until melted and smooth. Let cool for about 5 minutes.
To the melted chocolate, add in the sugar and stir well, followed by the eggs, one at a time, stirring well after each addition, and the vanilla. Add in the flour and cocoa powder, then stir in 1/2 cup of the beer concentrate. Pour the batter into the prepared pan evenly and bake for 30-35 minutes or until a toothpick inserted near the center comes out clean or with moist but not wet crumbs.
Once the brownies come out of the oven, brush about 2-3 Tablespoons of beer concentrate over the warm brownies. Then prepare your frosting.
In another saucepan, melt the butter and add the pecans, stirring gently to lightly toast. Add in the cocoa powder and stir to combine. Remove from heat. Add in one cup of the confectioners' sugar, stirring well, followed by a little of the remaining beer concentrate. Repeat with remaining confectioners' sugar and beer concentrate. Pour the frosting evenly over the warm brownies and let cool completely before cutting into squares.