Line two 8-inch round cake pans with parchment rounds and lightly grease the sides. Preheat the oven to 345°F (175°C).
Bloom the cocoa: In a medium bowl, whisk the sifted cocoa with the hot coffee until smooth and glossy. Set aside for 5 minutes to intensify the chocolate flavor.
In a large bowl, whisk together the granulated sugar, brown sugar, oil, sour cream, vanilla, and vinegar until the mixture looks thick and satiny. Whisk in the eggs and yolk just until combined; do not overmix.
In a separate bowl, whisk the flour, baking powder, baking soda, and salt. Stir the cocoa-coffee mixture into the wet ingredients, then add the dry ingredients in two additions, folding gently with a spatula until no dry streaks remain. Let the batter rest for 5 minutes to hydrate.
Divide the batter evenly between the pans (about 600–650 g per pan). Tap pans firmly on the counter to release large air bubbles.
Bake for 25–30 minutes (about 27 minutes on average), until a toothpick inserted in the center comes out with a few moist crumbs. Cool in pans 10 minutes, then turn out onto racks to cool completely. For easier frosting, chill the cooled layers for 15–20 minutes.
Make the frosting: Beat the butter in a stand mixer on medium speed for 2 minutes until creamy. Add cream cheese and beat 2 minutes more, scraping the bowl. Mix in cocoa, vanilla, and salt. Add powdered sugar in 3 additions, alternating with splashes of cream, beating 2–3 minutes until fluffy and spreadable. If needed, chill frosting 10 minutes to firm slightly.
Assemble: Level cake tops if needed. Place the first layer on a serving plate and spread about 1 cup frosting over it. Top with the second layer. Apply a thin crumb coat over the entire cake and chill 10 minutes, then finish with a thicker coat of frosting. Add sprinkles or shaved chocolate, if using.