Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper for easy removal.
In a large mixing bowl, combine the mashed bananas and peanut butter until smooth.
Add the granulated sugar, brown sugar, eggs, and vanilla extract to the banana mixture. Mix well until fully combined.
In a separate bowl, whisk together the baking soda, salt, and flour. Gradually add the dry ingredients to the wet ingredients, stirring just until combined. Do not overmix.
If using, fold in the chopped walnuts.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake in the preheated oven for 55-65 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.