Preheat the oven to 400°F. Grease a 10 x 15-inch jelly roll pan and set it aside.
In a saucepan, combine the butter, shortening, water, and cocoa powder. Bring to a boil over medium heat, whisking just until the butter and shortening melt, then remove from the heat.
In a large bowl, whisk together the sugar, flour, baking soda, and salt.
Pour the hot cocoa mixture over the dry ingredients and beat with an electric mixer on medium speed for 1 minute.
Add the eggs, buttermilk, and vanilla. Beat on medium speed for 1 minute more. The batter will be thin and pourable, which is exactly what you want.
Pour the batter into the prepared pan and tap it on the counter a few times to release air bubbles.
Bake for 20 to 23 minutes, until a toothpick inserted in the center comes out clean.
Set the pan on a wire rack. If the cake domed at all, gently press the top flat with a clean towel while it's warm so the frosting won't run off the sides. Leave the cake in the pan and make the frosting right away.