In a large bowl, using an electric mixer, beat butter until light and fluffy. Add the white and brown sugar. Beat well.
Add the egg, egg whites, and vanilla; beat until well blended.
Add mashed banana and beat on high speed for about 30 seconds.
Into a medium bowl, combine flour, baking soda, salt, and baking powder. Add flour mixture into butter and banana mix a little at a time, alternating with the heavy cream.
Pour batter evenly into a greased 9x5x3 inch loaf pan.
Bake at 350°F for about 1 hour 15 minutes or until browned and a toothpick inserted into the center comes out clean.
Cool bread in pan on wire rack 10 minutes. Then remove from pan and cool completely on wire rack.