Set the oven to preheat to 350 F. Grease then line a standard size loaf pan (9x5 inches) with parchment paper.
Make the pound cake batter: add the softened butter and sugar to the bowl of a stand mixer. Affix the paddle attachment and set the speed to medium low. Cream until several shades lighter, and airy - adding the salt and vanilla while it beats. This will take at least 3 minutes but up to five. Add the room temperature eggs and beat until smooth. Sift in the cake flour and add the baking powder. Add the sour cream and beat on low until smooth.
Make the brownie batter: set the butter and sugar in a microwave safe bowl and heat until the butter has melted, about 1 minute. Whisk well then return the bowl to heat for an additional 30 seconds. Add the cocoa and whisk until the batter starts to clump together. Crack in the egg and whisk until smooth. Add the flour and stir. Chop the chocolate very finely and stir until incorporated.
Layer the batters: add about a third of the pound cake batter into the pan, smoothing it into an even layer. Add half of the brownie batter and use an offset spatula to spread it into one layer. Add another third of the pound cake batter, smooth it over. Add the remaining brownie batter and spread evenly. Dollop the rest of the pound cake batter on top and carefully, covering the brownie batter completely (it will burn if exposed) spread it.
Bake the cake until a cake tester comes out clean, about an hour. The cake is not a high riser. Once baked, let cool briefly in the pan then transfer to a cooling rack. Serve warm or at room temperature. Store leftovers in an airtight container.