Place rack in center of oven and preheat oven to 350 degrees F.
Place a cupcake liner into each section of an 8-cupcake tin. Whisk together flours, cocoa, baking soda and salt in a medium bowl and reserve. Combine sour cream and buttermilk in a small bowl and reserve. Combine butter, oil and brown sugar in the bowl of a stand mixer and mix on high speed, scraping down sides of bowl, until sugar has dissolved and mixture is light in color, about 1 minute. Add egg and egg white and beat an additional 1 minute. Add 1/3 of flour-cocoa mixture, then 1/3 sour cream buttermilk mixture, mixing well after each addition. Repeat with remaining dry and wet ingredients. Distribute batter evenly among 8 cupcake tins. Bake for 15 to 17 minutes, or until a toothpick inserted into cupcake comes out clean. Let cupcakes cool slightly, transfer to wire racks and cool completely, 10 to15 minutes.
Combine confectioners' sugar and milk in a small saucepan and heat over low heat until sugar is dissolved. Add chocolate and stir until melted and icing is the consistency of thick pancake batter; add more milk if necessary. While still warm, top each cupcake with 1 1/2 to 2 teaspoons icing. Let icing harden completely, about 10 minutes.
Place cream cheese in a small microwave-save bowl and microwave on high for approximately 10 to 15 seconds, until cream cheese is melted but before it begins to bubble. Add confectioners' sugar and stir until sugar is dissolved. Let mixture cool slightly and transfer to a small plastic bag. Snip just the very bottom corner of the bag, then force icing to bottom of bag. Pipe a squiggle of icing down the center of each cupcake.