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 flour, sugar, cocoa powder, baking soda, baking powder, and salt.
In a separate bowl, whisk together the buttermilk, vegetable oil, eggs, and 2 teaspoons vanilla extract until smooth.
Add the wet ingredients to the dry ingredients and mix until just combined.
Carefully stir in the boiling water until the batter is smooth and thin.
Pour the batter evenly into the prepared sheet pan.
Bake for 28 to 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 cream cheese frosting: In a medium bowl, beat the softened cream cheese and butter together until smooth and creamy.
Add the powdered sugar gradually, beating on low speed until combined.
Add 1 teaspoon vanilla extract and 2 tablespoons milk, then beat on medium-high speed until the frosting is light and fluffy.
Once the cake is completely cooled, spread the cream cheese frosting evenly over the top.
Slice into 12 squares and serve.