Preheat oven to 350°F (175°C) with the rack in the center position. Grease two 9-inch round cake pans, line the bottoms with parchment paper, grease the parchment, then dust the pans with cocoa powder and tap out the excess.
In a large mixing bowl, whisk together the flour, sugar, cocoa powder, baking soda, baking powder, and salt for about 30 seconds until evenly combined with no lumps or streaks.
Add the eggs, buttermilk, oil, and vanilla extract to the dry ingredients and beat with a whisk or electric mixer on medium speed for 2 minutes, scraping down the sides and bottom of the bowl to ensure everything is fully incorporated.
Slowly pour the steaming hot coffee into the batter while stirring gently — the batter will become thin and liquidy, similar to pancake batter, which is exactly right. Stir just until fully combined.
Pour the batter evenly between the prepared pans, tap each pan on the counter 2–3 times to release air bubbles, then bake for 30–35 minutes until a toothpick inserted in the center comes out with just a few moist crumbs.
Let the cakes cool in the pans on wire racks for 10 minutes, then run a knife around the edges, invert onto racks, peel off the parchment, and let cool completely (at least 1–2 hours) before frosting.
Beat the softened butter for 2 minutes until creamy, then alternate adding the sifted sugar-cocoa mixture with the heavy cream and vanilla, beating on medium-high for 3–4 minutes until light and fluffy; adjust consistency with more cream or powdered sugar as needed.
Level the cake layers if domed, spread about 1 cup of frosting over the first layer, stack the second layer on top, apply a thin crumb coat, refrigerate 15–20 minutes to set, then apply the remaining frosting to the top and sides.