1. Preheat the oven to 350°. In a small bowl, whisk together 2 tablespoons each of the flour and cocoa powder. Butter two 9-inch round cake pans and line the bottoms with parchment paper. Butter the paper and dust the pans with the cocoa-flour mixture, tapping out the excess.
In a medium bowl, whisk the 2 cups of flour and 1/4 cup of cocoa powder with 1/2 cup of the granulated sugar, and the baking powder, baking soda and salt.
In the bowl of a standing electric mixer fitted with the whisk, beat the eggs with the brown sugar and the remaining 1/2 cup plus 1 tablespoon of granulated sugar at medium-high speed until thickened, about 5 minutes. At medium speed, gradually add 1/2 cup of the oil and beat for 3 minutes. Beat in the melted chocolate, then add the remaining oil in a thin stream, until thoroughly blended, scraping the side and bottom of the bowl. At low speed, beat in the buttermilk and vanilla. Remove the bowl
Pour the cake batter into the prepared pans and bake in the center of the oven for about 25 minutes, until a toothpick inserted in the centers of the cakes comes out with a few moist crumbs attached. Cool the cakes in the pans for 20 minutes, then invert them onto a rack to cool completely. Peel off the parchment paper.