Place banana slices, brown sugar, and 1 tablespoon butter in an 8-inch square baking dish.
Bake for 35 minutes, stirring after 17 minutes. Cool slightly. Reduce the oven temperature to 375°.
Lightly spoon cake flour into dry measuring cups; level with a knife. Combine flour, baking soda, and baking powder in a medium bowl. Set aside.
In another medium bowl, combine banana mixture, buttermilk, and vanilla. Set aside.
In a large mixing bowl, using an electric mixer on medium speed, mix together the butter and granulated sugar until well blended.
Add eggs to sugar mixture and mix well. Add flour mixture to sugar mixture to alternating with banana mixture, beginning and ending with flour mixture.
Pour batter into a 13 x 9–inch baking pan coated with baking spray. Bake for 20 minutes or until a wooden pick inserted in center comes out clean.
Cool completely in pan on a wire rack. .
To prepare frosting
Melt butter in a small saucepan over medium heat; cook 4 minutes or until lightly browned. Cool slightly.
Combine browned butter, powdered sugar, cream cheese, and 1 teaspoon vanilla in a medium bowl; beat with a mixer until smooth.
Spread frosting over cooled bars. Sprinkle with pecans.