Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch sheet pan.
In a medium bowl, whisk together the flour, sugar, baking soda, and salt.
In a small saucepan, combine the melted butter, water, and cocoa powder. Heat over medium heat, stirring until smooth and just beginning to boil. Remove from heat.
Pour the cocoa mixture into the dry ingredients and stir to combine.
In a separate bowl, whisk together the buttermilk, eggs, and vanilla extract.
Add the buttermilk mixture to the batter and stir until smooth and fully combined.
Pour the batter into the prepared sheet pan and spread evenly.
Bake for 28 to 32 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 large bowl, beat the softened cream cheese and butter together until smooth and creamy.
Gradually add the powdered sugar, one cup at a time, beating well after each addition.
Add the vanilla extract and beat until the frosting is light and fluffy.
Once the cake is completely cool, spread the cream cheese frosting evenly over the top.
Cut into 12 squares and serve.