Preheat oven to 350ºF. Line three 8-inch round cake pans with parchment paper and spray with cooking spray.
In a double boiler,** combine the chocolate, cocoa powder, and hot water, stirring until smooth. Add 1/2 cup of the sugar to the chocolate mixture and stir until thick and glossy. Remove from heat and set aside to cool.
In a medium bowl, whisk together the flour, baking soda, and salt. Combine the buttermilk and vanilla in a glass measuring cup.
In the bowl of a stand mixer fitted with a whisk attachment, whisk the whole eggs and egg yolks on medium speed until combined. Add the remaining 1 1/4 cups sugar, increase speed to high, and continue whisking until lightened in color and fluffy, about 2 to 3 minutes. Add the cooled chocolate mixture to the egg mixture and stir on medium until fully incorporated, pausing to scrape down the sides of the bowl.
Add the softened butter, 1 Tablespoon at a time, mixing for about 10 seconds after each addition. Add 1/3 of the flour mixture followed by 1/2 of the buttermilk mixture, mixing until incorporated. Repeat process with remaining flour mixture and buttermilk mixture until batter is thoroughly combined. Scrape down the sides of the bowl and give one last stir before dividing batter equally among the three prepared pans. Lightly tap pans against the countertop to settle any batter and to eliminate any air bubbles.
Bake cakes for 30-34 minutes, or until a toothpick inserted into the center comes out with a few crumbs attached. Remove cakes from the oven and allow to cool in the pan for 15 minutes on a wire rack. Run a knife around the edge of the cakes, carefully flip them out onto a wire rack, peel off the parchment paper, then flip the cakes right side up. Cool completely.