Preheat oven to 350 degrees.
Add the butter and sugar to the bowl of an electric mixer and cream on medium speed for 2-3 minutes, occasionally scraping down the sides.
Add the egg and beat for an additional 2 minutes.
Sift together the dry ingredients and add half to the butter mixture, beating on low until just mixed.
Pour in the milk and mix on low until incorporated before adding the rest of the flour mixture.
Scrape down the sides of the bowl and mix until just incorporated.
Pour batter into a thoroughly greased 8x8 baking dish and set aside while you make the syrup.
Add the water, brown sugar and cocoa to a small saucepan and bring to a boil. Boil for 1 minute, watching to make sure it does not boil over.
Pour syrup over the batter and bake on the center rack of the oven for 30 minutes.
Serve warm. Top with a dollop of cream, creme fraiche or vanilla ice cream, if desired.