Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch sheet pan.
In a large bowl, whisk together the flour, granulated sugar, salt, baking soda, and 1/2 cup cocoa powder until well combined.
In a medium saucepan, combine the 1 cup butter and 1 cup water. Bring to a boil over medium heat, stirring occasionally.
Pour the hot butter and water mixture over the dry ingredients and mix until combined.
In a small bowl, whisk together the buttermilk, eggs, and 1 teaspoon vanilla extract.
Add the buttermilk mixture to the batter and stir until smooth and fully incorporated.
Pour the batter into the prepared sheet pan and spread evenly.
Bake for 30 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare the frosting: In a medium bowl, combine the powdered sugar, 1/4 cup cocoa powder, softened butter, milk, and 1 teaspoon vanilla extract. Beat until smooth and creamy.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Spread the frosting evenly over the warm cake.
Allow the cake to cool completely before slicing and serving.