Preheat your oven to 350℉. Grease or line your cake pan or springform pan with parchment paper.
Sift the sugar, flour, cocoa powder, baking soda, and baking powder into a mixing bowl.
Make a well in the dry mix and pour in the coffee, buttermilk, oil, egg, and vanilla. Mix well to combine; it'll be a thin-seeming batter.
Pour the batter into your cake pan. Bake for 35-40 minutes until a toothpick in the center comes out clean.
Remove the cake from the oven and let cool for at least 20 minutes before trying to remove it from the pan. Then, let it finish cooling on a cooling rack or counter.
Make the frosting by beating together the cocoa powder and butter until it's smooth. Add in the powdered sugar, vanilla, and most of the milk, and beat until it's a fluffy consistency. If it's too thick, add more milk a tbsp at a time.
Frost the cake, cut a slice, and enjoy!