Preheat the oven to 350 degrees F. Grease the edges of two 9-inch round cake pans. Dust with flour and tap out the excess. Line the bottom of each pan with a circle of parchment paper.
Melt the chopped chocolate with the water in a heatproof bowl set over a pot of simmering water. Stir until smooth, then set aside until it cools to room temperature.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and 1 1/4 cup of the sugar until light and fluffy, about 5 minutes. Beat in the melted chocolate. Add the egg yolks, one at a time.
In a medium bowl, stir together the flour, baking powder, baking soda and salt. Mix in half of the dry ingredients into the creamed butter mixture beating on low speed until incorporated. Mix in the buttermilk and the vanilla until combined. Mix in the remaining dry ingredients.
In a clean dry bowl of an electric mixer fitted with the whisk attachment, beat the egg whites until the form soft, droopy peaks. Slowly add the remaining 1/4 cup of sugar and continue beating until stiff peaks form. Using a rubber spatula, fold about one-third of the egg whites into the cake batter to lighten it. Then fold in the remaining egg whites just until incorporated.
Divide the batter between the prepared cake pans and bake for 45 minutes, until a toothpick inserted into the center comes out clean. Allow to cool in the pans for 10 minutes, then remove from pans and transfer to a wire rack to cool completely.