Preheat the oven to 350°F. Grease a 9" x 13" pan., For the cake: Place the cocoa in a large mixing bowl and pour the hot coffee (or water) over it. Mix until smooth, then add the oil and buttermilk and mix to combine., Add the baking soda and salt, beat for 30 seconds, then add the vanilla and eggs. Mix until smooth. Add the sugar and flour and beat for 2 minutes at medium speed. Scrape the bowl, beat for 30 seconds more, then pour into the prepared pan., Bake for 33 to 35 minutes, until the top springs back when lightly pressed and the edges just begin to pull away from the pan. Remove from the oven and cool for 30 minutes on a rack, then put in the freezer for at least 1 hour., To make the buttercream: Beat the butter and salt together until pale and fluffy. Add the confectioners' sugar and vanilla and beat until the frosting is fluffy, then add 1 tablespoon of milk (or half & half) as needed for a smooth consistency. Transfer the frosting to a piping bag with a 1/2" round tip. Chill for 5 to 10 minutes before piping if really soft., Pipe the buttercream across the cake's shorter (9") dimension in seven 1/2"-diameter strips, edge to edge across the cake. The lines should be 1" apart. Return to the freezer for at least 30 minutes to set the buttercream., To make the fudge frosting: In a medium saucepan with a heavy bottom, combine the buttermilk, dark corn syrup, butter, cocoa, and salt over medium heat. Bring to a boil and cook for 2 to 3 minutes, until the bubbles make a snapping sound as they pop. Turn the heat to low and whisk in the confectioners' sugar. Whisk until the sugar melts and the mixture is smooth and glossy. Remove from the heat, stir in the vanilla, and pour into a large glass measuring cup. Set aside to cool until just slightly warm., To finish: Remove the cake from the freezer and pour half of the warm fudge frosting over the cake in long, even strokes to cover the buttercream bumps completely. Tilt the pan to let the frosting flow over the cake, if necessary, to cover the top., Return the pan to the freezer to 5 to 10 minutes. Repeat with the rest of the frosting to completely cover the bumps and the cake. If the frosting is too thick, heat it in 5-second bursts in the microwave, stirring until smooth and pourable. Return the cake to the refrigerator for another 20 minutes to set the frosting before cutting., Store this cake in the refrigerator until ready to serve. It will keep, covered and refrigerated, for up to 1 week.