Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt.
In another bowl, cream the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually mix in the dry ingredients, alternating with the buttermilk and espresso.
Pour the batter into the prepared pan and bake for 25-30 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.