Butter two 9-inch cake pans, then line the bottoms with rounds of parchment or wax paper. Preheat the oven to 350°.
Melt both chocolates together with the 6 tablespoons of water. Use either a double-boiler or a microwave. Stir until smooth, then set aside until room temperature.
In the bowl of an electric mixer, or by hand, beat the butter and 1 ¼ cup of the sugar until light and fluffy, about 5 minutes. Beat in the melted chocolate, then the egg yolks, one at a time.
Sift together the flour, baking powder, baking soda, and salt.
Mix in half of the dry ingredients into the creamed butter mixture, then the buttermilk and the vanilla extract, then the rest of the dry ingredients.
In a separate metal or glass bowl, beat the egg whites until they hold soft, droopy peaks. Beat in the ¼ cup of sugar until stiff.
Fold about one-third of the egg whites into the cake batter to lighten it, then fold in the remaining egg whites just until there's no trace of egg white visible.
Divide the batter into the 2 prepared cake pans, smooth the tops, and bake for about 45 minutes, until a toothpick inserted into the center comes out clean.
Cool cake layers completely.
While the cakes are baking and cooling, make the filling, syrup, and icing.