Preheat oven to 350°F. Line a 9x9x2" metalbaking pan with foil, leaving a 2" overhang.Bring stout to a boil in a medium saucepan;cook until reduced to 1/2 cup, about12 minutes.
Let cool. Reserve 1/4 cup stout.
Stir 12 ounces chocolate and 1 cup butter ina medium metal bowl set over a saucepan ofsimmering water until melted and smooth.
Whisk sugar, eggs, and vanilla in a largebowl to blend. Gradually whisk in chocolatemixture, then 1/4 cup stout from pan. Foldin flour and 1 1/4 teaspoons salt.
Pour batter intoprepared pan.
Bake brownies until surface beginsto crack and a tester inserted into centercomes out with a few moist crumbsattached, 35–40 minutes.
Transfer panto a wire rack and let cool for at least20 minutes. Stir remaining 4 ounces chocolatein a medium metal bowl set over a saucepanof simmering water until melted andsmooth.
Add reserved 1/4 cup reduced stout,remaining 2 tablespoons butter, and 1/4 teaspoon salt;whisk until well blended.
Pour warm glaze over brownies.
Letstand at room temperature until glaze is set,about 40 minutes. DO AHEAD: Can be made8 hours ahead. Cover and let stand at roomtemperature.
Using foil overhang, lift brownie frompan; cut into squares.
