Make the brownies: Preheat the oven to 350 degrees F. Line a 9-by-13-inch baking dish with foil, leaving a 2-inch overhang on the two short ends; coat with cooking spray. Bring the beer to a simmer in a large saucepan over medium heat and cook until reduced to about 1/3 cup, about 15 minutes. Pour into a bowl and set aside.
Wipe out the saucepan and add the butter and chopped chocolate. Cook over medium-low heat, stirring, until smooth. Remove from the heat and let cool slightly, about 5 minutes. Add the granulated sugar and eggs and stir until glossy and smooth. Stir in the reduced beer. Add the flour, cocoa powder and salt and stir until no lumps remain. Stir in the chocolate chips.
Pour the batter into the prepared pan. Bake until a toothpick inserted into the middle comes out clean, 30 to 35 minutes. Transfer the pan to a rack. Meanwhile, make the glaze: Mix 2 tablespoons beer with the granulated sugar in a small bowl until the sugar is dissolved; spoon or brush over the warm brownies and set aside.
Make the icing: Combine the butter, all but 2 tablespoons pecans and the salt in a medium saucepan over medium heat. Cook, stirring, until the butter is melted and the nuts are lightly toasted, about 5 minutes. Add the cocoa powder and stir until smooth. Remove from the heat and add the confectioners' sugar in two batches, alternating with the remaining 1/4 cup beer. Stir until smooth, then pour over the warm brownies and gently spread. Sprinkle with the remaining 2 tablespoons pecans. Let cool completely. Lift the brownies out of the pan using the foil overhang and cut into pieces.