Preheat the oven to 350°F (175°C). Lightly grease a 9x5 inch loaf pan.
In a separate bowl, whisk together the dry ingredients: flour, baking soda, and salt.
In another bowl, whisk the mashed bananas with the melted butter, then beat in the sugar, egg, and vanilla until smooth.
Stir the wet ingredients into the dry ingredients just until moistened; fold in the walnuts.
Pour the batter into the prepared loaf pan and bake for 60–65 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Cool in the pan on a rack for 10 minutes, then unmold and cool completely before slicing.
Notes
Feel free to swap walnuts with pecans or stir in chocolate chips for a different texture. Use very ripe bananas for maximum sweetness and moistness.Store the cooled loaf in an airtight container at room temperature for several days, or freeze slices for longer storage.