Preheat the oven to 350°F (175°C) and grease an 8x12 inch sheet pan.
Combine butter, water, cocoa powder, and sugar in a saucepan. Bring to a boil over medium heat, stirring constantly until the mixture is smooth and glossy, about 2 minutes. Remove from heat and set aside.
1 cup unsalted butter, 1/2 cup unsweetened cocoa powder, 1 cup water, 2 cups granulated sugar
In a large mixing bowl, sift together flour, salt, and baking soda. Add eggs, vanilla, buttermilk, and the hot cocoa mixture. Stir until just combined and smooth.
2 cups all-purpose flour, 1/2 teaspoon salt, 1 teaspoon baking soda, 2 large eggs, 1 teaspoon vanilla extract, 1/2 cup buttermilk
Pour batter into the prepared sheet pan, spreading evenly with a spatula. Bake for about 20 minutes, or until a toothpick inserted into the center comes out clean. Let cool on a wire rack.
While the cake cools, prepare the frosting by melting butter and cocoa powder together in a small saucepan over low heat. Remove from heat and whisk in powdered sugar and milk until smooth and glossy. Spread the frosting evenly over the cooled cake.
3/4 cup unsweetened cocoa powder, 1/4 cup butter, 2 cups powdered sugar, 1/4 cup milk
Allow the frosting to set for 15-20 minutes before slicing and serving. The cake should be moist with a shiny, fudgy top and a dense crumb.
