Preheat oven to 350°.
To prepare cake, coat 2 (8-inch) round cake pans with cooking spray; line bottoms with wax paper. Coat wax paper with cooking spray.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, and salt in a small bowl, stirring well with a whisk. Place granulated sugar, oil, 1 1/4 teaspoons vanilla extract, egg whites, and egg in a large bowl; beat with a mixer at medium speed until well blended. Add mashed banana; beat well. Add flour mixture and buttermilk alternately to sugar mixture, beginning and ending with flour mixture.
Pour batter into prepared pans. Bake at 350° for 35 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on wire racks; remove from pans. Peel off wax paper; cool completely on wire racks.
To prepare frosting, place cream cheese and 1 teaspoon vanilla extract in a large bowl; beat with a mixer at medium speed until fluffy. Add powdered sugar; beat at low speed until smooth.
Place 1 cake layer on a plate; spread with 1/2 cup icing, and top with other cake layer. Spread remaining icing over top and sides of cake. Sprinkle pecans and coconut over top of cake. Store cake loosely covered in refrigerator.