Preheat oven to 350°F Grease a 13x9 inch metal baking pan.
In a medium bowl, combine flour, baking powder and salt.
In a large bowl, using electric mixer, beat butter and granulated and brown sugars until light and fluffly. Beat in vanilla. Add eggs and bananas, beating well. Add flour mixture and beat just until combined. Fold in chocolate chips and walnuts.
Spread batter in prepared pan. Bake in preheated oven for 30 to 35 minutes or until light golden brown and starting to pull away from sides of pan. The center will be slightly soft to the touch.
Let cool completely in pan or rack. Cut into bars.