Preheat the oven to 350°F Spray an 8-inch square baking dish with vegetable spray.
Make filling: in a food processor or bowl with an electric mixer, beat together the cream cheese, sugar, milk and vanilla until the mixture is smooth. Set it aside.
Make the cake: in a large bowl, mix together brown sugar, sour cream, oil, whole egg and egg white. In a separate bowl, stir together flour, cocoa and baking powder. Add the liquid ingredients to the dry ingredients, blending just until everything is mixed.
Pour half the cake batter into a prepared dish. Spoon the filling on top; spread it with a wet knife. Pour the remaining batter into the pan. Bake for 20 to 25 minutes or until it is just barey loose in the centre.