Sift the flours together with the cocoa into a small bowl. Melt the butter and chocolate in a bowl placed over a medium saucepan filled with simmering water, stirring until smooth. You could also do this in the microwave.
Remove the bowl from heat and mix in the 2/3 cup sugar, then the eggs. Mix in the flour and cocoa mixture and beat vigorously with a wooden spoon until the batter becomes smooth and glossy. Spread half the brownie mixture evenly in the prepared pan. In a separate bowl, beat together the cream cheese, the egg, 1/4 cup of sugar and vanilla extract until smooth. You could also do this step in a food processor.
Dollop the cream cheese alternately with the remaining brownie mixture over the batter in the pan, then take a knife or spatula (or even a chopstick) and gently swirl the cream cheese mixture with the chocolate batter.
Bake in the preheated 180°C/350°F oven for 35 to 45 minutes, or until the batter in the centre of the pan is just set. Leave the brownie in the switched off oven with the door slightly ajar for a further 15 minutes. Cool on a wire rack, then lift the brownie out of the tin and peel away the foil. Cut the brownies into squares or bars. These will keep in an airtight container for a couple of days. They also freeze well.