Lightly grease an 20cm square baking pan. In a large bowl, cream together the butter, white sugar and 1/4 cup brown sugar. Beat in the egg until well blended. In a medium bowl, combine the flour, baking powder, bicarb soda and 1/2 teaspoon cinnamon. Stir the flour mixture into the creamed mixture alternately with buttermilk. Spread evenly into the prepared baking pan.
In a small bowl mix 1/4 cup brown sugar, walnuts and 1/4 teaspoon cinnamon. Sprinkle over the batter. Cover and refrigerate overnight.
The next day, preheat oven to 180 degrees C. Bake the cake for 40 to 45 minutes in the preheated oven, or until a toothpick inserted in the centre comes out clean.