Lightly grease an 8 inch 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, baking 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 350 degrees F (175 degrees C). Bake the cake for 40 to 45 minutes in the preheated oven, or until a toothpick inserted in the center comes out clean.