Preheat oven to 350°F (175°C). Grease a standard 9×5-inch loaf pan. For easier removal, line the bottom with parchment paper.
In a large mixing bowl, mash the bananas until mostly smooth.
Add the egg, vanilla extract, brown sugar, granulated sugar, and cinnamon. Stir until well combined.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Add the dry ingredients to the banana mixture and stir gently until just combined.
Fold in the melted butter or applesauce. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top.
Bake the healthy banana bread for 35–45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the loaf to cool in the pan for 5–10 minutes before transferring to a wire rack to cool completely.