In a small bowl, stir together flour, baking soda and salt; set aide.
In a small saucepan, combine butter and brown sugar. Bring to a boil over low heat, stirring constantly. Immediately remove from heat and stir in 1 cup of the chocolate chips until melted and smooth. Blend in vanilla. Transfer mixture to a large mixing bowl and cool slightly. With wire whisk, beat in eggs one at a time. Blend in mashed banana, then flour mixture. Fold in remaining 1/2 cup chocolate chips and walnuts. Spread in pan.
Bake about 45 minutes.
Cool completely in pan.
Lightly sift powdered sugar over top before cutting into bars.