Preheat oven to 375°F. Grease a 9- by 13-inch cake pan with butter. Add cocoa powder to pan and shake to coat the pan. Shake out any excess cocoa.

Mix the cocoa and coffee in a mixing bowl using a stand mixer or hand mixer; beat on medium speed for 30 seconds. Add oil, mix for 30 seconds; add buttermilk, mix for 30 seconds; add baking soda, mix for 30 seconds; add salt, mix for 30 seconds; add vanilla, mix for 30 seconds; add eggs, mix for 30 seconds; add sugars, mix for 30 seconds. Add flour and mix about 5 minutes until the batter is lump free (though the batter will have bubbles in it).

Pour batter into the prepared pan and smooth it out with a spatula. Bake until cake tester comes out clean, 35 to 40 minutes. Transfer to a wire rack and allow to cool for at least 30 minutes. Transfer the cake to the freezer for at least an hour and up to overnight.

In the bowl of your mixer, beat butter, heavy cream, and vanilla on medium low speed. With the mixer on low, slowly add powdered sugar, beating on low until just mixed. Increase speed to high and beat for one minute until smooth. Using a large round piping tip, pipe frosting in lines across the surface of the cake, an inch or so apart. Place cake back in the freezer for 30 minutes to an hour.

In a large bowl whisk together buttermilk, confectioner's sugar and vanilla.

In a medium saucepan, combine, sugar, cocoa, corn syrup, salt and 1 stick worth of butter. Stir occasionally to fully incorporate butter as it's melting then bring mixture to a boil over medium high heat. Cook until the mixture is 240°F on a candy or instant read thermometer (a bit dropped into cold water will make a soft, malleable ball), then take off the heat.

Whisking constantly, pour the hot mixture into the buttermilk mixture. Add the remaining butter and continue whisking until the mixture is smooth and has cooled slightly.

Take the cake out of the freezer and pour the slightly warm frosting over the cake; cover buttercream rolls completely. The frosting will be thin, but will firm up when cool. Tilt the cake pan to get frosting everywhere. Return cake to freezer for at least 30 minutes more to set.

Serve chilled; a small paring knife works best to cut the cake. Store leftovers in refrigerator or freezer.