Preheat oven to 350°F. Adjust the oven rack to the middle position. Butter two 9-inch round cake pans with 2-inch high sides. Dust pans with flour and knock out any excess. Set aside.
In a medium heatproof bowl combine the unsweetened chocolate, cocoa and hot water. Set the bowl over a saucepan with 1-inch of simmering water. Do not let the bowl touch the water. Stir with a spatula until completely melted, about 3 minutes. Add ½ cup of granulated sugar and stir until the mixture is thick and glossy. Remove from the hot water and set aside to cool.
In a separate medium bowl whisk together the flour, baking soda and salt; set aside. In a 2-cup measuring cup with a spout whisk together the buttermilk, vegetable oil and vanilla; set aside.
In the bowl of a stand mixer fitted with the whisk attachment, whisk the eggs and medium-low speed until combined. Add the remaining ½ cup of granulated sugar and all the brown sugar. Turn the mixer speed to high and whisk until the mixture is thickened, lighter in color and fluffy, about 3 to 4 minutes.
Replace the whisk with the paddle attachment. Add the cool chocolate mixture and blend until incorporated scraping down the sides and bottom of the bowl as needed with a rubber spatula. Add the softened butter one tablespoon at a time mixing well after each addition before adding the next.
Next add one-third of the flour mixture then half the buttermilk blending well after each addition. Repeat adding half the remaining flour, then all remaining buttermilk and finally add the last of the flour mixture. Scrape down the sides and bottom of the bowl and fold a few times with a spatula to ensure all flour is incorporated. Divide the batter evenly between the prepared cake pans.
Bake the cakes until a toothpick inserted in the center comes out with no wet batter, about 28 to 35 minutes. Don’t over-bake! Moist crumbs are good. Cool the cakes in the pans for 15 minutes then invert onto a wire cooling rack. Cool completely before icing.