Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch sheet pan.
In a large mixing bowl, sift together the all-purpose flour, granulated sugar, 3/4 cup cocoa powder, baking powder, baking soda, and salt.
Add the buttermilk, vegetable oil, eggs, and 2 teaspoons vanilla extract to the dry ingredients. Beat on medium speed until well combined.
Reduce the mixer speed to low and carefully add the boiling water to the batter. Mix 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 prepare the frosting, beat the softened butter in a medium bowl until creamy.
Gradually add the powdered sugar and 1/2 cup cocoa powder, alternating with the whole milk, beating on low speed until smooth and spreadable.
Stir in 2 teaspoons vanilla extract.
Spread the frosting evenly over the cooled cake.
Cut the cake into 24 squares and serve.