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Preheat the oven to 350 degrees. Spray 2 9-inch round cake pans with cooking spray. Line the bottoms of the pans with parchment, then spray the parchment with cooking spray. Lightly dust with flour and set pans aside.
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Combine the stout and butter in a medium saucepan set over medium heat and bring to a simmer. Remove pan from the heat and whisk in the cocoa powder until mixture is smooth. Set aside to cool for 5 minutes.
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Whisk the flour, sugar, baking soda, and salt together in a large mixing bowl. In a separate large bowl, whisk the sour cream and eggs together.
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Stir the stout mixture into the sour cream mixture and whisk until combined. Fold the flour mixture into the stout mixture with a rubber spatula until the batter is smooth and free of lumps.
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Divide batter evenly between the prepared pans and bake 35 to 40 minutes, until a toothpick inserted into the center of the cakes comes out clean. Cool completely on a wire rack before frosting.