Preheat oven to 350 degrees F (175 degrees C). Grease a 9 inch pie plate.
In a medium bowl, cream together the butter and sugars until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Mix in the baking powder and salt. Gradually stir in the mashed bananas, then fold in the flour.
Pour batter into prepared pie plate. Bake for 30 to 35 minutes, or until center is set. Cool before serving.
Top with ice cream or whipped cream for an extra special treat!