Cream oil with 1/3 cup of sugar. Combine in separate bowl sifted flour, baking powder and salt. Add dry ingredients, 1/4 cup at a time, alternately with milk, into oil mixture, begin and end with dry ingredients. Beat about 30 seconds or until smooth after each addition. Combine the egg, remaining 1/3 cup of sugar and vanilla and beat until thick. Fold into batter. Spread chopped nuts over bottom of a lightly greased 8 inch square pan. Carefully pour ion batter and bake at 350ºF. for 30 - 35 minutes. Cool for 10 minutes. Cut in squares.