Prep the pans: Preheat oven to 350°F (175°C). Line the bottoms of two deep 8‑inch round cake pans with parchment paper, then lightly grease and flour the sides.
Mix the dry ingredients: In the bowl of a stand mixer (or large mixing bowl), whisk together flour, both sugars, cocoa powder, baking soda, and salt until evenly combined.
Add the fats: Pour in the melted butter and oil. Stir until the mixture looks sandy and well blended.
Incorporate eggs and flavoring: Add the eggs, extra yolk, and vanilla extract. Mix until smooth, scraping down the sides and bottom of the bowl as needed.
Blend in the liquids: Gradually add the buttermilk, mixing until fully incorporated. Then slowly pour in the hot coffee, stirring until the batter is glossy and uniform.
Bake the cakes: Divide the batter evenly between the prepared pans. Bake for 35–40 minutes, or until a toothpick inserted in the center comes out with moist crumbs.
Cool and frost: Let cakes cool in the pans for 15 minutes, then invert onto a wire rack to cool completely. Spread frosting over one layer, stack with the second, and finish frosting the entire cake. Slice and serve.