Preheat your oven to 350 degrees Fahrenheit and grease a loaf pan with butter or cooking spray.
In a large mixing bowl, combine the mashed bananas and sugar. Mix well until the sugar is dissolved.
Add the melted butter and beaten eggs to the banana mixture. Stir until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Add the dry ingredients to the banana mixture and gently fold until just combined. Be careful not to overmix, as it can result in a dense bread.
Stir in the vanilla extract and chopped walnuts. The walnuts add a delightful crunch and nutty flavor to the bread.
Pour the batter into the greased loaf pan and smooth the top with a spatula.
Bake in the preheated oven for 60-70 minutes, or until a toothpick inserted into the center comes out clean. The baking time may vary, so keep an eye on the bread after the 50-minute mark.
Once baked, remove the banana bread from the oven and let it cool in the pan for 10 minutes. Then transfer it to a wire rack to cool completely before slicing and serving.