Preheat the oven to 350°F (175°C). Grease a 9x13 inch baking pan with butter or non-stick spray.
In a saucepan over medium heat, melt the butter. Once melted, remove from heat and whisk in sugar, cocoa powder, and salt until smooth and glossy.
1 cup buttermilk, 1 cup unsweetened cocoa powder, 0.5 teaspoon salt
In a large mixing bowl, sift together flour and baking soda. Add eggs, vanilla extract, and buttermilk, stirring until combined. Pour in the hot water and mix until smooth. The batter will be thin.
2 cups all-purpose flour, 1 teaspoon baking soda, 2 large eggs, 2 teaspoons vanilla extract, 1 cup buttermilk, 1 cup hot water
Gradually pour the warm chocolate mixture into the batter, stirring constantly to incorporate everything evenly. The batter will be thin but homogeneous.
2 sticks unsalted butter
Pour the batter into the prepared baking pan, spreading evenly. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out with moist crumbs. The surface should be firm and slightly shiny when done.
While the cake cools slightly, prepare the frosting by beating the softened butter, powdered sugar, milk, and vanilla together until smooth and creamy. Once the cake has cooled, spread the frosting evenly over the top. Allow the frosting to set before slicing.
1 cup powdered sugar, 0.5 cup butter, 3 tablespoons milk, 1 teaspoon vanilla extract
