Preheat your oven to 325°F (160°C). Coat a 9x5-inch loaf pan with non-stick cooking spray and set aside.
In a large mixing bowl, beat the softened butter and sugar together until the mixture becomes crumbly, about 2 minutes.
Add the egg and egg white one at a time, beating well after each addition. Increase to high speed and beat until the mixture is light and fluffy.
Stir in the mashed bananas, unsweetened applesauce, honey, and vanilla extract. Mix until well combined.
In a separate bowl, whisk together the all-purpose flour, whole wheat flour, baking soda, and salt. Gradually add the dry ingredients to the banana mixture, stirring just until moistened. Avoid overmixing to keep the bread tender.
Pour the batter into the prepared loaf pan. Smooth the top and sprinkle evenly with chopped pecans.
Bake for 60-65 minutes, or until a toothpick inserted into the center comes out clean. If the top begins to brown too quickly, cover it loosely with foil during the last 10-15 minutes of baking.
Cool in the pan for 10 minutes before transferring the loaf to a wire rack to cool completely.