Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan.
In a large mixing bowl, sift together the flour, granulated sugar, 3/4 cup cocoa powder, baking powder, baking soda, and salt.
In a separate bowl, whisk together the buttermilk, vegetable oil, eggs, and 2 teaspoons vanilla extract until well combined.
Add the wet ingredients to the dry ingredients and mix until smooth.
Carefully stir in the boiling water until the batter is thin and well combined.
Pour the batter evenly into the prepared baking 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.
While the cake cools, prepare the frosting by creaming the softened butter in a medium bowl until smooth.
Gradually add the powdered sugar and 1/3 cup cocoa powder, alternating with the milk, beating until the frosting is smooth and spreadable.
Stir in 1 teaspoon vanilla extract.
Once the cake is completely cooled, spread the frosting evenly over the top.
Cut the cake into 24 squares and serve.