Preheat oven to 350 degrees and line an 8x8 baking pan with parchment paper.
Pour beer into a measuring cup and let rest so foam can subside. Make sure you have a full cup of liquid.
Place chocolate and butter in the bowl of a double boiler or in a metal bowl set tightly over a saucepan of simmering water. Stir until chocolate and butter are both melted.
Remove from heat and using a hand mixer, beat in sugar. Allow mixture to cool to lukewarm.
In a separate medium bowl, whisk together flour and cocoa powder.
When chocolate mixture is lukewarm, beat in eggs until mixture looks glossy. Stir in chocolate stout.
Fold in flour mixture until well-combined, taking care not to over-mix.
Pour brownie batter into prepared pan and bake for 20-24 minutes, until a toothpick comes out sticky, but not wet.
Let cool in pan before removing from pan and cutting into squares. Lightly dust with confectioners' sugar if desired.