Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the flour, sugar, cocoa powder, baking soda, baking powder, and salt. Whisk them together until well mixed.
Add the eggs, buttermilk, vegetable oil, and vanilla extract to the dry ingredients. Mix until just combined.
Slowly pour in the hot coffee while stirring the batter. The batter will be quite thin, which is completely normal.
Pour the batter into the prepared 9x13 inch baking pan. Bake in the preheated oven for 30-35 minutes or until a toothpick inserted in the center comes out clean.
Once baked, remove the cake from the oven and let it cool in the pan for about 10 minutes. Then transfer it to a cooling rack to cool completely.
In a medium bowl, beat the softened butter until creamy. Gradually add the cocoa powder and powdered sugar, mixing until combined. Pour in the coffee and vanilla extract, and beat until smooth and fluffy.
Once the cake is completely cool, spread the frosting evenly over the top.