Preheat oven to 350 degrees F. Butter two 6-inch round cake pans and line with parchment paper. Set aside.
In a small bowl, combine unsweetened chocolate, cocoa powder and boiling water. Whisk until smooth. Set aside and allow to cool. It is ready to use when it is no longer hot, and just warm to the touch.
In the bowl of a stand mixer fitted with a paddle attachment, cream together butter and brown sugar until fluffy and smooth. Add eggs and mix until incorporated. Add sour cream and vanilla and continue to mix.
In a medium bowl, whisk together all-purpose flour, cake flour, baking powder and salt. Add 1/3 of flour mixture into the bowl of stand mixer. Mix at low speed until almost combined. Pour in half of the cooled chocolate mixture and mix. Add another 1/3 of flour, followed by the remaining half of chocolate. End with the last 1/3 of flour. Mix between each addition and scrape down bowl as needed to ensure thorough mixing.
Divide batter evenly between prepared cake pans. Bake for 30 minutes, rotating pans after 15 minutes. Bake until cake is set and toothpick inserted in center of cake comes out clean. Let cake cool in pan for 5 minutes. Run a knife or mini offset spatula around the perimeter of the cake to loosen it from the pan. Invert and let cake cool to room temperature on a wire rack.