Preheat the oven to 350°F (175°C). Grease a 9×13 inch sheet pan and set aside.
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 over medium heat, combine 1 cup butter and 1 cup water. Bring to a boil, then immediately remove from heat.
Pour the hot butter and water mixture into the dry ingredients and stir until combined.
In a separate small bowl, whisk together the buttermilk, eggs, and 1 teaspoon vanilla extract.
Add the buttermilk mixture to the batter and mix 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 saucepan, combine 1/4 cup butter, 1/4 cup cocoa powder, powdered sugar, and milk.
Heat over medium heat, stirring constantly until the mixture is smooth and begins to bubble.
Remove from heat and stir in 1 teaspoon vanilla extract.
Allow the frosting to cool slightly until it thickens but is still pourable.
Once the cake is done, remove it from the oven and immediately pour the frosting evenly over the hot cake.
Use a spatula to spread the frosting evenly over the cake surface.
Allow the cake to cool completely before slicing and serving.