Preheat oven to 180 degrees C. Grease and flour 2 23cm round pans. Sift together the plain flour, cake flour, bicarb soda, salt and green tea powder; set aside.
In a large bowl, beat together sugar, oil and eggs until smooth. Stir in 1 1/2 teaspoons vanilla. Beat in the flour mixture alternately with the yoghurt, mixing just until incorporated. Pour batter into prepared pans.
Bake in the preheated oven for 30 to 40 minutes or until a toothpick inserted into the centre of the cake comes out clean. Cool on wire rack for 30 minutes before turning out of the pans.
To make Green Tea icing: Sift together icing sugar and green tea powder. In a medium bowl combine tea mixture with butter, cream cheese, vanilla and milk. Beat with an electric mixer until smooth.
To assemble the cakes: when the cakes are completely cooled put one layer on a flat serving plate. Spread a thin layer of icing over it. Place the other layer of cake on top and spread icing to cover the top and sides of cake. Dust with green tea powder if desired. Serve cold or at room temperature.