Preheat oven 350 degrees F.
Spray two 9 inch round cake pans with flour-added cooking spray, or rub with shortening and dust with cocoa powder.
Sift (I actually didn’t sift) the cake flour, baking soda, and salt into bowl of a stand mixer and mix well. Add softened butter to flour mixture and mix on low speed with the paddle until the butter coats the flour. Stop occasionally to scrape sides of bowl. Add the brown sugar, cooled melted chocolate, sour cream, vanilla and *half* of the water. Continue mixing on low speed until well blended, scraping sides of bowl. Then beat on medium speed for about a minute.
To the eggs in the separate bowl, add the remaining half cup of water (or coffee) and beat with a fork or whisk. With the mixer on low, gradually pour the egg/water mixture into the batter. Continue running mixer for about 3 minutes on medium speed, scraping sides until you get a smooth, velvety batter.
Pour batter into the prepared cake pans and bake on center rack at 350 degrees F for about 35 minutes or until cakes test done. If your pans are black, you might want to use 325 F for 40 minutes.
Sour cream Frosting
Melt the butter in a saucepan over medium heat. Reduce heat to low and add chocolate. Stir over low heat or residual heat until chocolate melts. Remove from stove and let cool slightly (about 10 minutes). Stir the sour cream into the chocolate.
Sift half of the powdered sugar into bowl of a stand mixer fitted with whisk attachment. Add the chocolate mixture and stir until smooth. Stir in vanilla. Add the rest of the powdered sugar and beat mixture until smooth, adding water as needed.