Preheat the oven to 400 degrees F (200 degrees C). Grease and flour a 10x15-inch cake pan.
Mix flour, sugar, and baking soda together in a large bowl; set aside.
Heat butter, water, cocoa powder, and vanilla extract in a saucepan over medium heat, stirring occasionally, until smooth and just boiling. Pour over the flour mixture and stir to combine. Stir in buttermilk and eggs. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 20 minutes. Remove cake from the oven and cool on a wire rack for 5 minutes.
Meanwhile, combine butter, milk, cocoa powder, and vanilla extract for the icing in a saucepan over medium heat. Bring to a slow boil, then stir in powdered sugar. Pour icing over the hot cake. Let sit for 2 hours before serving.