Preparation

Preheat oven to 350°F. Lightly grease a 9×13-inch baking pan and set aside. Clear a spot in your freezer where the pan can sit flat.

Make the cake

In a large bowl, whisk together flour, sugar, cocoa, baking soda, and salt. In a medium bowl, whisk together the 1/2 cup oil, buttermilk, coffee, eggs, and vanilla until well combined. Add to flour mixture, and whisk again until completely incorporated. Transfer batter to prepared pan, and spread out evenly. Bake until the cake bounces back in the center when pressed, about 30 to 35 minutes. Set aside to let cool completely. (If cake isn’t cooled completely, the piped buttercream will risk melting.)

Make the vanilla buttercream

In a large bowl, beat butter with an electric mixer on medium speed for 1 minute. Add confectioners’ sugar, milk, vanilla, and salt, and continue beating for 2 minutes more. Transfer to a piping bag fitted with a 1/2-inch round tip. Working across the short side of the cake, evenly pipe 10 stripes of buttercream down the length of the cake, leaving a roughly 1-inch gap in between the stripes. Freeze cake, uncovered, until buttercream is very firm, about 1 hour.

Make the chocolate fudge icing

In a medium pot over medium heat, melt butter. Whisk in cocoa powder, buttermilk, corn syrup, and salt until well combined. Bring to a rolling boil. Cook, whisking gently, for 2 minutes. Remove from heat, and whisk in confectioners’ sugar and vanilla until completely smooth and silky. Set aside, stirring occasionally, to let cool until warm (not hot) but still pourable, about 5 minutes.

Remove cake from the freezer, and pour over the icing in wide, even ribbons to cover it completely. (Avoid spreading the frosting with a knife, as it should form valleys in between the lines of buttercream, rather than being flat on top. If needed, you can work quickly to tilt the pan to distribute the icing.) If remaining icing in the pot becomes too stiff to pour, temporarily refreeze the cake and return the pot to medium-low heat briefly to soften until pourable again.
Chill cake in the refrigerator to allow the icing to set completely, about 1 hour, before serving.