Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan or line it with parchment paper.
In a large mixing bowl, combine the mashed bananas, eggs, unsweetened applesauce, Greek yogurt, and vanilla extract. Mix well until smooth.
In a separate bowl, whisk together the whole wheat flour, baking soda, baking powder, ground cinnamon, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
If using, fold in the chopped walnuts.
Pour the batter into the prepared loaf pan and spread it evenly.
Bake in the preheated oven for 55 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the banana bread from the oven and allow it to cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing.