Preheat your oven to 350°F (175°C) and grease a 15×10-inch jelly roll pan or a 9×13-inch baking dish. For easy removal, consider lining with parchment paper, allowing a slight overhang on the sides.
In a large bowl, whisk together the flour, sugar, baking soda, and salt. This uniform distribution of dry ingredients prevents pockets of baking soda that could create bitter spots in your finished cake.
In a medium saucepan over medium heat, combine the butter, oil, cocoa powder, and water. Bring to a boil while stirring continuously to prevent scorching.
Pour the hot chocolate mixture over the dry ingredients and mix until just combined.
In a separate bowl, whisk together the eggs, buttermilk, vanilla extract, and vinegar until smooth. Fold this mixture into the batter until fully incorporated.
Pour the batter into your prepared pan and bake for 20-25 minutes, or until a toothpick inserted in the center comes out clean with a few moist crumbs.
While the cake bakes, combine butter, cocoa powder, and milk in a saucepan. Bring to a gentle boil, then remove from heat. Stir in vanilla extract and gradually add powdered sugar, whisking until smooth and glossy.
Pour the warm frosting over the cake while it's still warm (about 10 minutes out of the oven). This crucial timing allows the frosting to penetrate slightly into the top layer, creating that signature melt-in-your-mouth quality. If using nuts, sprinkle them evenly over the top now.
Allow the cake to cool for about 15 minutes before slicing and serving.