Prepare the cake layers by preheating the oven to 350°F, greasing two 9-inch cake pans, and lining them with parchment rounds.
Make the stout-butter mixture by simmering the stout and butter in a saucepan, then adding cocoa powder and letting it cool.
Whisk together flour, sugar, baking soda, and salt in a bowl. In another bowl, whisk sour cream and eggs. Combine the stout-butter mixture with the egg mixture and then add the flour mixture. Divide the batter between pans and bake until done.
Prepare the Salted Dark Chocolate Pudding by combining milk, cornstarch, sugar, chocolate, cocoa powder, vanilla, and salt in a saucepan, cooking until thickened.
Prepare the Dark Chocolate Pudding Buttercream by mixing butter, confectioners’ sugar, cocoa powder, dark chocolate pudding, and salt until creamy and fluffy. Adjust consistency with cream or sugar.
Frost the cake with the Dark Chocolate Pudding Buttercream once the cake layers have cooled.