Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch sheet pan.
In a large bowl, sift together the flour, sugar, 3/4 cup cocoa powder, baking soda, baking powder, and salt.
In a separate medium bowl, whisk together the buttermilk, vegetable oil, eggs, and 2 teaspoons vanilla extract until combined.
Add the wet ingredients to the dry ingredients and mix until smooth.
Carefully stir in the boiling water until fully incorporated. The batter will be thin.
Pour the batter evenly into the prepared sheet pan.
Bake for 30 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool completely in the pan on a wire rack.
To make the frosting, cream the softened butter and 4 tablespoons cocoa powder together in a large bowl until smooth.
Add the milk and 1 teaspoon vanilla extract and mix until combined.
Gradually add the powdered sugar, beating until the frosting is smooth and spreadable.
Spread the frosting evenly over the cooled cake.
Cut into 12 squares and serve.