Preheat oven to 350°.
Combine brown sugar and 2 teaspoons flour; set aside.
Lightly spoon flour into dry measuring cups; level with a knife.
Combine 1 1/3 cups flour and next 7 ingredients in a medium bowl; stir with a wire whisk. Make a well in center of mixture. Combine banana and next 3 ingredients; add to flour mixture, stirring just until moist.
Spoon batter into an 8-inch square baking pan; sprinkle with brown sugar mixture.
Pour 1 1/2 cups boiling water over batter (do not stir). Bake at 350° for 40 minutes or until pudding is bubbly and cake springs back when lightly touched in center. Serve warm. Divide onto individual serving dishes and top with ice cream.