Preheat the oven to 160˚C/gas mark 3. Grease and line a 20cm square cake tin.
Sift the flours and cocoa powder into a bowl.
In a second bowl, beat the sugar and butter together until soft and smooth. Spoon in the tahini and stir it through. Add the vanilla extract, then the eggs, and beat until well combined. Fold the flour and cocoa powder mixture into the batter, then add the milk. Add the chocolate chips last and mix until just combined.
Pour the batter into the prepared tin and bake for 35 to 40 minutes, until a toothpick inserted into the centre comes out clean.
Remove from the oven and allow to cool in the tin for 15 minutes. Remove the cake from the tin and place on a wire rack to let it cool completely before slicing or storing. Serve with some tahini dribbled over.