Preheat the oven to 350 degrees F and line an 8 x 8 baking pan with parchment (alternatively, you can grease thoroughly.
In a large bowl, combine together the dry ingredients (flour, sugar, cocoa, baking soda)
Melt the butter and allow to cool.
In a medium sized bowl, whisk together the buttermilk, coffee, melted butter and vanilla.
Lightly beat the egg and add to the buttermilk mixture.
Make a well in the dry ingredients and add the buttermilk mixture.
Mix thoroughly until well combined.
Pour batter into the greased baking pan and bake for 30 minutes.
Remove cake from oven and check for done-ness by inserting a toothpick into the center of the cake, it should come out clean, with no streaks of batter.
Cool the cake (still in the pan) on a rack until completely cool before frosting with vanilla buttercream.
BUTTERCREAM
Using an electric mixer, whip together the butter, sugar, and vanilla.
Add the milk until desired consistency is reached.