Preheat oven at 190°C/370°F. Grease and flour a springform 20cm/8 inches pan.
Beat together all-purpose and whole wheat flour, sugar, butter, eggs, vanilla and milk until smooth and creamy. Pour the batter into the prepared pan and arrange the apple slices on top. Bake for 35 minutes or until the center is firm.
Remove it from the oven, sprinkle with the cinnamon-sugar and walnuts, and top it with the butter cubes. Bake for another 20 minutes, or until a toothpick inserted in the center comes out clean.