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Preheat oven to 350°. Line a 9x9x2" metal baking pan with parchment paper, leaving a 2" overhang. Bring stout to a boil in a medium saucepan; cook until reduced to 1/2 cup, about 12 minutes. Let cool. Reserve 1/4 cup stout.
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Combine 12 ounces of chocolate chips and butter in a large glass bowl and microwave until melted in 30 second intervals, stirring after each.
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Add eggs, stirring to combine.
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Add vanilla.
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Add sugar, whisking to combine.
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Gradually whisk in 1/4 cup stout from pan.
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Gently fold in flour and 1 1/4 tsp. salt.
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Pour batter into prepared pan.
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Bake brownies until a few crumbs cling to a tester, about 35-40 minutes.
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Transfer pan to a wire rack and let cool for at least 20 minutes. Put remaining 1/2 cup of chocolate in a glass bowl and microwave until melted, in 30 second intervals, stirring after each.
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Add reserved 1/4 cup reduced stout, remaining 2 Tbsp. butter, and 1/4 tsp. salt; whisk until well blended.
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Pour warm glaze over brownies. Let stand at room temperature until glaze is set, about an hour.
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Using parchment paper overhang, lift brownie from pan; cut into squares.