These are so seriously dark and rich that you can't eat very many of them, but every single molecule counts. This recipe is based on the "Guinness Brownies" from Sally's Baking Addiction and the "Chocolate Stout Cupcakes" from King Arthur Flour. You can also make root-beer brownies--they're awfully good, too. I give info for that variation in the notes.
In a small saucepan, bring the Guinness or stout to a boil over medium-high heat. Once boiling, reduce to medium heat and allow to simmer until reduced down to 2/3 cup, about 20-22 minutes. This is kind of a fussy process, as you have to pour the reducing beer into a heatproof measuring cup to see how far down it has gone. It can take several tries to get it reduced enough. Set aside to cool for at least 10 minutes. You will use 1/2 cup in the brownies and the rest in the frosting if you are making the powdered-sugar version. If you're making the ganache frosting, then I'd just go ahead and boil down the beer to 1/2 cup, which will make it a little stronger but not unacceptably so.
I make these brownies specifically for receptions, so I use mini-muffin pans, the ones that have 24 wells per pan. I buy small foil liners and spray the insides with a quick spritz of cooking spray. If you want to just make a pan of brownies, use a 9x9 size and line with foil, leaving an overhang to facilitate removal. If you're doing that, it's also a good idea to spritz the foil.
Preheat oven to 350 degrees.
Place the butter in a microwave-safe bowl that's big enough to mix the whole batch of batter and microwave on 50% power for 2 minutes, then check to see if the butte has melted. You may need another 30 seconds to a minute--do 30 seconds at a time. Put the chocolate, chopped or just broken into squares, into the melted butter and let sit until partially melted, then stir the mixture until the chocolate is completely melted and smooth, Again, as above, you may need to do an additional 30 seconds or so. Be sure to use 50% power and not high! Whisk in the sugar and 1/2 cup of reduced Guinness until completely combined. Whisk in the eggs and vanilla extract. Finally, whisk in the flour, salt, and espresso powder (if using). The batter will be thick and shiny. I then use a small "disher"--the 1 tablespoon size--to scoop the batter into the individual muffin wells. If you're using a regular pan, just spread the batter evenly in the pan.
Bake 10-15 minutes for the individual mini brownies and 30-35 minutes for a panful. A toothpick should come out with a few moist crumbs clinging to it. Don't overbake! You want the brownies to be moist.
Let cool, the frost. I think these do need the frosting, as on their own they're not very sweet. See below for your frosting choices.
To make root beer brownies, use the same amount of root beer as beer, boiling it down as indicated. Root beer extract in the place of vanilla will intensity the root beer flavor, of course, but isn't absolutely necessary.