1. Preheat oven to 350F. Grease and flour a 10-cup tube or Kuglehopf pan.
2. Combine flour, baking soda, baking powder and salt.
3. In an electric mixer, beat butter and shortening until creamy, about 2 minutes. Add brown sugar, white sugar and beat 1 more minute. Add eggs, beating after each addition. Add mashed bananas and vanilla, beat well. Add the flour mixture, and cornmeal alternately with the sour cream, mixing until just incorporated. Pour batter into prepared pan. Bake 55-60 minutes or until batter is firm. Cool 15 minutes. Invert onto a plate or cake stand. Dust with powdered sugar.