Step 1: Preheat your oven to 350°F (175°C). Grease and flour a 9x5 inch loaf pan, or line with parchment paper.
Step 2: In a medium bowl, whisk together the flour, baking soda, cinnamon, and salt. Set aside.
Step 3: In a large bowl, mash the ripe bananas until mostly smooth. A few lumps are fine.
Step 4: Add the melted butter, granulated sugar, brown sugar, and vanilla extract to the mashed bananas. Whisk until well combined.
Step 5: Whisk in the eggs one at a time until fully incorporated into the banana mixture.
Step 6: Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix; a few streaks of flour are acceptable.
Step 7: Gently fold in the toasted and chopped walnuts.
Step 8: Pour the batter into the prepared loaf pan, spreading evenly.
Step 9: Bake for 55-65 minutes, or until a wooden skewer inserted into the center comes out clean. If the top browns too quickly, loosely tent with aluminum foil.
Step 10: Remove the banana nut bread from the oven and let it cool in the pan on a wire rack for 10-15 minutes. Then, carefully remove from the pan and transfer to the wire rack to cool completely before slicing and serving.